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Seminorms on ordered vector spaces that extend to Riesz seminorms on larger Riesz spaces

Onno van Gaans
<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jqdttgmkdfelzpwxohdz7agdwy" style="color: black;">Indagationes mathematicae</a> </i> &nbsp;
As a generalization of the notion of Riesz seminorm, a class of seminorms on directed partially ordered vector spaces is introduced, such that (1) every seminorm in the class can be extended to a Riesz  ...  seminorm on every larger Riesz space that is majorized and (2) a seminorm on an order dense  ...  The author wants to thank A.C.M. van Rooij and C.D. Aliprantis for their help and encouragement.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0019-3577(03)90067-x">doi:10.1016/s0019-3577(03)90067-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vm7myi2jd5cmfa3a7djdhpbqtq">fatcat:vm7myi2jd5cmfa3a7djdhpbqtq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190416145137/https://core.ac.uk/download/pdf/82000589.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cb/e8/cbe8da82dd33930b8ca9d929c37457182d522f29.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0019-3577(03)90067-x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

A Characterization of the Boolean Prime Ideal Theorem in Terms of Forcing Notions [article]

David Fernández-Bretón, Elizabeth Lauri
<span title="2016-09-09">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For certain weak versions of the Axiom of Choice (most notably, the Boolean Prime Ideal theorem), we obtain equivalent formulations in terms of partial orders, and filter-like objects within them intersecting  ...  certain dense sets or antichains.  ...  to be a linear functional extending f .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1609.02630v1">arXiv:1609.02630v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xzi7b5i7gffuzbxrbqlwfzovve">fatcat:xzi7b5i7gffuzbxrbqlwfzovve</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200915073707/https://arxiv.org/pdf/1609.02630v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/15/0b/150bdce1527cee18e7f6cb8f4dc4f3c98c16f9cc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1609.02630v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Representation of partially ordered linear algebras

Richard C. Metzler
<span title="1974-09-01">1974</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hjoli2j6qffdpaalkszryuidk4" style="color: black;">Bulletin of the American Mathematical Society</a> </i> &nbsp;
The standard completion procedure for Archimedean ordered linear spaces shows that A is isomorphic with an order dense subspace of a Dedekind complete linear lattice D.  ...  Thus D is a linear lattice pola and the order density of shows (since 1 is easily seen to be a weak order unit for A) that the image of 1 is a weak order unit for D.  ...  The standard completion procedure for Archimedean ordered linear spaces shows that A is isomorphic with an order dense subspace  of a Dedekind complete linear lattice D.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9904-1974-13585-8">doi:10.1090/s0002-9904-1974-13585-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/udqavfkxzjcctdbfydr77fj6su">fatcat:udqavfkxzjcctdbfydr77fj6su</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170827161040/http://www.ams.org/journals/bull/1974-80-05/S0002-9904-1974-13585-8/S0002-9904-1974-13585-8.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/42/d2/42d2a781d10b1b1400f1686e54675a872a6dfeab.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9904-1974-13585-8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

The vector lattice cover of certain partially ordered groups

G. Buskes, A. Van Rooij
<span title="">1993</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qucxg3yndjaptj6krclryhveua" style="color: black;">Journal of the Australian Mathematical Society</a> </i> &nbsp;
In this paper we introduce the notion of Riesz homomorphism on Archimedean directed partially ordered groups and use it to study the vector lattice cover of such groups. 1991 Mathematics subject classification  ...  Then (j> extends uniquely to an order preserving linear map <f>: E -> F. If <f> is a Riesz homomorphism, then so is PROOF.  ...  Then the restriction of co to QG" is a complete Riesz homomorphism. QG is order dense in E, so <u| QG extends to an increasing map <f>: E -* F. Then < > is a complete Riesz homomorphism.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s1446788700031839">doi:10.1017/s1446788700031839</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/krtzugvz2fg3zcqtxhmrufmdnm">fatcat:krtzugvz2fg3zcqtxhmrufmdnm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20181030061500/https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7C3E3B7F869B3C426892795D57B600F1/S1446788700031839a.pdf/div-class-title-the-vector-lattice-cover-of-certain-partially-ordered-groups-div.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b6/d3/b6d383d912db8493140a7a4c0e995bcb411dcf24.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s1446788700031839"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> cambridge.org </button> </a>

More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures [article]

Dana Bartosova
<span title="2012-04-04">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
ordering.  ...  In this paper, we compute universal minimal flows of groups of automorphisms of uncountable ω-homogeneous graphs, K_n-free graphs, hypergraphs, partially ordered sets, and their extensions with an ω-homogeneous  ...  Acknowledgement I wish to thank Stevo Todorčević for proposing the project of computing universal minimal flows of groups of automorphisms of uncountable structures, for introducing me to Jónsson structures  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1204.0037v2">arXiv:1204.0037v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vqbtrz5utfegvdyq63zcjs55qm">fatcat:vqbtrz5utfegvdyq63zcjs55qm</a> </span>
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The $k$-norm extension property for Banach spaces

Henry B. Cohen
<span title="1964-05-01">1964</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a64sw4kcsveajhudnssdwrwvze" style="color: black;">Proceedings of the American Mathematical Society</a> </i> &nbsp;
And B has the norm extension property (k-norm extension property) iff any continuous linear operator into B from a subspace of a inseparable) normed linear space Y can be extended to a linear operator  ...  We say that B is k-separable iff B has a dense ¿-subset.  ...  Let w he an element not in B and extend the ordering of 5UP to a partial ordering of Y=S^J jwjUTby decreeing 5 S {w} S T.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9939-1964-0169023-2">doi:10.1090/s0002-9939-1964-0169023-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uku7swiwcfdmdnny6b2omhcspm">fatcat:uku7swiwcfdmdnny6b2omhcspm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180719000135/http://www.ams.org/journals/proc/1964-015-05/S0002-9939-1964-0169023-2/S0002-9939-1964-0169023-2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/56/0e/560e8483a534e52c5bd6e95784f1570a408060b4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9939-1964-0169023-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Page 62 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 45, Issue 1 [page]

<span title="">1939</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_american-mathematical-society-bulletin" style="color: black;">American Mathematical Society. Bulletin of the American Mathematical Society </a> </i> &nbsp;
The order-preserving image of a continuous partially ordered set is shown to be continuous.  ...  The principal object of this monograph is the definition and discussion of continu- ity in dense partially ordered sets. Foradori first defines continuity in a simply ordered set.  ... 
<span class="external-identifiers"> </span>
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Extending monotone seminorms on partially ordered vector spaces

Onno van Gaans
<span title="">1998</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jqdttgmkdfelzpwxohdz7agdwy" style="color: black;">Indagationes mathematicae</a> </i> &nbsp;
Given a monotone seminorm on a directed partially ordered vector space, the question arises whether it can be extended to a monotone seminorm on the Dedekind completion.  ...  This paper presents a necessary condition and proves it to be sufficient for existence of a largest extension on any partially ordered vector space that contains the given space as a majorizing subspace  ...  If p can be extended to a monotone seminorm on some Riesz space containing E, thenp extends to a monotone seminorm on any partially ordered vector space containing E as a majorking linear subspace.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0019-3577(98)80003-7">doi:10.1016/s0019-3577(98)80003-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vaup57j4inbmph24rdrqn7aqry">fatcat:vaup57j4inbmph24rdrqn7aqry</a> </span>
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Book Review: Grundgedanken der Teiltheorie

H. M. MacNeille
<span title="1939-01-01">1939</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hjoli2j6qffdpaalkszryuidk4" style="color: black;">Bulletin of the American Mathematical Society</a> </i> &nbsp;
The order-preserving image of a continuous partially ordered set is shown to be continuous.  ...  The principal object of this monograph is the definition and discussion of continuity in dense partially ordered sets. Foradori first defines continuity in a simply ordered set.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9904-1939-06927-9">doi:10.1090/s0002-9904-1939-06927-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nzs4ljx3zffvlcukixdly5tjj4">fatcat:nzs4ljx3zffvlcukixdly5tjj4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200322052359/https://www.ams.org/journals/bull/1939-45-01/S0002-9904-1939-06927-9/S0002-9904-1939-06927-9.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/95/b7/95b7ee0a6f64c0611b3967e4cd1df4decd6b709b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9904-1939-06927-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Book Review: Introduction à la Mécanique Non-Linéaire

W. J. Trjitzinsky
<span title="1939-01-01">1939</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hjoli2j6qffdpaalkszryuidk4" style="color: black;">Bulletin of the American Mathematical Society</a> </i> &nbsp;
The order-preserving image of a continuous partially ordered set is shown to be continuous.  ...  The principal object of this monograph is the definition and discussion of continuity in dense partially ordered sets. Foradori first defines continuity in a simply ordered set.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9904-1939-06925-5">doi:10.1090/s0002-9904-1939-06925-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ee3wxze3qva4fdtoynoi44ktzy">fatcat:ee3wxze3qva4fdtoynoi44ktzy</a> </span>
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A Survey on Temporal Logics [article]

Savas Konur
<span title="2011-04-25">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This work was partially supported by EPSRC research project EP/F033567.  ...  This axiomatic system can be extended for the classes of discrete linear orderings, dense linear orderings, etc. [68] .  ...  Partial-order temporal logics are suitable to express partial orderings representing the behaviour of concurrent systems [111] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1005.3199v3">arXiv:1005.3199v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nogsv2iggvd5likbkrnmnzpsdu">fatcat:nogsv2iggvd5likbkrnmnzpsdu</a> </span>
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Riesz* homomorphisms on pre-Riesz spaces consisting of continuous functions

Hendrik van Imhoff
<span title="2017-08-30">2017</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nqjml422pndvnfwrrcbrws7vqq" style="color: black;">Positivity (Dordrecht)</a> </i> &nbsp;
We extend this result to Riesz* homomorphisms on order dense subspaces of C(X ). On those subspace we consider and compare various classes of operators that extend the notion of a Riesz homomorphism.  ...  In particular, we characterize the automorphism group for order dense subspaces of C(X ).  ...  Our aim is to extend the above theorem to partially ordered vector subspaces of C(X ).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11117-017-0519-4">doi:10.1007/s11117-017-0519-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bpma4wflznabdiyw2ooh3gczze">fatcat:bpma4wflznabdiyw2ooh3gczze</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190503145648/https://link.springer.com/content/pdf/10.1007%2Fs11117-017-0519-4.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/68/e9/68e9ed17d4eb2d02daed91f88f4be283c26d5f1c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11117-017-0519-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Utility representation of lower separable preferences

Özgür Yılmaz
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/voowybrx3nfvlmrxrcu5ixa3wa" style="color: black;">Mathematical Social Sciences</a> </i> &nbsp;
Our results extend the main representation theorems by Ok (2002) in terms of the separability axioms.  ...  By the classical Szpilrajn's Theorem (1930) , each partial order can be extended to a linear order.  ...  Thus, Theorem 4 extends his result to lower separable partial orders. a linear order, and an antichain if = ;: Clearly, if (X; <) is a chain, then o n= ;; and if it is an antichain, then o n= f(x; y) :  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.mathsocsci.2008.06.005">doi:10.1016/j.mathsocsci.2008.06.005</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ktaftyjvczfoxcstdqq7qtrtti">fatcat:ktaftyjvczfoxcstdqq7qtrtti</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20100702013917/http://home.ku.edu.tr:80/~ozyilmaz/Lower-Separability.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/60/ea/60eafad5b0616f0b3727fd1e3593ed7aa0012132.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.mathsocsci.2008.06.005"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Cohen-like first order structures [article]

Ziemowit Kostana
<span title="2020-12-08">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Among them, we are primarily interested in linear orders.  ...  We study forcing notions similar to the Cohen forcing, whichadd some struc-tures in given first-order language.  ...  It will be convenient to denote by Part (L, ≤) the set of finite, partial automorphisms of a linear order (L, ≤). Lemma 3.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2009.03552v3">arXiv:2009.03552v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kbac5px4gbadrcftvd2wyjekkm">fatcat:kbac5px4gbadrcftvd2wyjekkm</a> </span>
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A poset hierarchy

Mirna Džamonja, Katherine Thompson
<span title="">2006</span> <i title="Walter de Gruyter GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wckadx7nhvdhboiqdgx2dinqve" style="color: black;">Central European Journal of Mathematics</a> </i> &nbsp;
Partial orders such that for every a < b the set {x : a < x < b} has size ≥ κ are called weakly κ-dense, and posets that do not have a weakly κ-dense subset are called strongly κ-scattered.  ...  This article extends a paper of Abraham and Bonnet which generalised the famous Hausdorff characterisation of the class of scattered linear orders.  ...  In this paper, we use 'order' to denote a 'partial order', and whenever we deal with linear orders we specify this.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11533-006-0001-1">doi:10.1007/s11533-006-0001-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jqma3etotjbdnc45v2egixfspq">fatcat:jqma3etotjbdnc45v2egixfspq</a> </span>
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