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Topology via Logic

Marcelo P Fiore
<span title="">1999</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hq6x4whtd5hhlhsxzculyeamey" style="color: black;">Science of Computer Programming</a> </i> &nbsp;
Topology via Logic (Cambridge University Press) 0 521 36062 5 hardback, 0 521 57651 2 paperback Background and scope of the book. Domain theory (see [7] for a recent discussion) is  ...  It is shown that the free frame over a set of generators subject to a set of relations always exists. This result is theoretically interesting and methodologically important.  ...  Theoretically, the situation is very much in contrast with the algebraic theory of complete boolean algebras, as free complete boolean algebras need not exist.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0167-6423(98)00020-3">doi:10.1016/s0167-6423(98)00020-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iga22thiybb6pe7goqwskfrw2y">fatcat:iga22thiybb6pe7goqwskfrw2y</a> </span>
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Soft Sets - Motivation and Overview

B.V.S.T. Sai, P.D.N. Srinivasu, N.V.E.S. Murthy
<span title="2019-12-30">2019</span> <i title="Research India Publications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/x7vq7yygtrdvxbmccivqkjeqaq" style="color: black;">Global Journal of Pure and Applied Mathematics</a> </i> &nbsp;
In this paper we present some of the main developments in the soft set theory as well as in the theory of algebraic structures and soft topology as a review of literature motivated by Molodsov.  ...  In his pioneering paper Soft Set Theory-First Results which was published in the journal Computers and Mathematics with Applications.  ...  In 2014 [95] , they constructed a soft topology over universe set X by assigning a topological structure to X and probed some interesting results in this context.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.37622/gjpam/15.6.2019.1055-1067">doi:10.37622/gjpam/15.6.2019.1055-1067</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q5nvpshfbbdzpgli35cyob3m7u">fatcat:q5nvpshfbbdzpgli35cyob3m7u</a> </span>
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Presheaves, Sheaves and their Topoi in Quantum Gravity and Quantum Logic [article]

Ioannis Raptis
<span title="2001-10-15">2001</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A brief synopsis of recent conceptions and results, the current status and future outlook of our research program of applying sheaf and topos-theoretic ideas to quantum gravity and quantum logic is presented  ...  to quantum gravity especially via his Abstract Differential Geometry theory [43, 44, 45, 46] , with Chris Mulvey (University of Sussex) on quantales and noncommutative topology, as well as a brief but  ...  Acknowledgments Exchanges with Chris Isham (Imperial College) on topoi and their potential application to quantum gravity, with Tasos Mallios (University of Athens) on sheaves and their possible application  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/gr-qc/0110064v1">arXiv:gr-qc/0110064v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kni7qpgc65cgte4qsiczclpvgq">fatcat:kni7qpgc65cgte4qsiczclpvgq</a> </span>
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Regularity of Ultrafilters, Boolean Ultrapowers, and Keisler's Order

Francesco Parente
<span title="">2019</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nxnim3i24fhcvkvgruk2dej7yu" style="color: black;">Bulletin of Symbolic Logic</a> </i> &nbsp;
In Chapter 2, we undertake a systematic study of regular ultrafilters on Boolean algebras.  ...  We then apply our analysis to the study of cofinal types of ultrafilters; as an application, we answer a question of Brown and Dobrinen by giving two examples of complete Boolean algebras on which all  ...  In our case, of course, a further generalization has been made by taking the consequence relation as many-valued also and this in turn gives rise to a generalization of the algebraic structure frame to  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/bsl.2019.57">doi:10.1017/bsl.2019.57</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2dmoxipznfa5hibm2ow6eoeoim">fatcat:2dmoxipznfa5hibm2ow6eoeoim</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200214050910/https://www.cambridge.org/core/services/aop-cambridge-core/content/view/28427F8B5EC02B6B65A27C83B9B187BA/S107989861900057Xa.pdf/div-class-title-regularity-of-ultrafilters-boolean-ultrapowers-and-keisler-s-order-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/0e/5c/0e5c14b7af038a451b14903d3491fa9fc74053b2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/bsl.2019.57"> <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>

Page 20 of Mathematical Reviews Vol. 56, Issue 1 [page]

<span title="">1978</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The main theorem has interesting applications in topological algebra. First the author uses it to obtain his earlier result (Quart. J. Math.  ...  The other main topological application is to the reviewer’s theory of varieties of topological algebras (in the sense of universal algebra ) [J. Austral. Math. Soc. Ser. A 23 (1977), no. 2, 207-241].  ... 
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Nonlinear and Noncommutative Mathematics: New Developments and Applications in Quantum Physics

M. Norbert Hounkonnou, S. Twareque Ali, Gerald A. Goldin, Richard Kerner, Kalyan B. Sinha, Akira Yoshioka
<span title="">2010</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dur7nzaqy5hezkanc3eeianfuy" style="color: black;">Advances in Mathematical Physics</a> </i> &nbsp;
We then present a review by Richard Szabo of some results in gauge theories and topological string theory.  ...  Lie groups and algebras, including diffeomorphism groups, gauge groups, and loop groups, together with some of their areas of application in mathematical physics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2010/497040">doi:10.1155/2010/497040</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jyrbznidlvh3flzzjhnwt6yxgq">fatcat:jyrbznidlvh3flzzjhnwt6yxgq</a> </span>
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Book Review: Topologie I. Espaces métrisables, espaces complets

G. T. Whyburn
<span title="1952-03-01">1952</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;
For example, the development and exploitation of the homotopy relation between mappings has very greatly extended the range of applicability of the set theoretic method and has rendered many results in  ...  Here the hand of the master is apparent and guides the reader on every page, presenting him with a perfectly organized and beautifully simple pathway to a large body of the deepest results in topology  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9904-1952-09601-4">doi:10.1090/s0002-9904-1952-09601-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/batlcvvgtnhi3fvz7eipcb3c74">fatcat:batlcvvgtnhi3fvz7eipcb3c74</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180726173051/http://www.ams.org/journals/bull/1952-58-02/S0002-9904-1952-09601-4/S0002-9904-1952-09601-4.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/2a/26/2a26b0ca5441ae4f7042b0fa4eca53ef3cf9db7b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9904-1952-09601-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

On Geometric Topological Algebras

A. Mallios
<span title="">1993</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7a65khxirfbfljbnqng5zzeslu" style="color: black;">Journal of Mathematical Analysis and Applications</a> </i> &nbsp;
As a result, one further considers the so-called "geometric topological algebras", having special cohomological properties, in terms of their "Gel'fand sheaves", being also of a particular significance  ...  It is proved that at the basis of this type of algebras lies the sheaf-theoretic notion of (functional) localization, which, in the particular case of a given topological algebra, refers to the respective  ...  We start, by first giving, in the next Section, the necessary preliminary material, as well as, the relevant results, concerning the sheaf-theoretic rudiments for the study of the topological algebras  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/jmaa.1993.1026">doi:10.1006/jmaa.1993.1026</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4awo5arywvgpfef7vt5c7sto54">fatcat:4awo5arywvgpfef7vt5c7sto54</a> </span>
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Page 5746 of Mathematical Reviews Vol. , Issue 98I [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The author gives a quick construction of the Adem relations in the mod 2 Steenrod algebra (actually he produces the re- lation Sq*~'Sq*, from which all the other Adem relations can be derived).  ...  Priddy, Topology 34 (1995), no. 3, 633-649; MR 96m:55028]. One of the main topological results is that if BP has no transfer summands, then P is a Swan group, while the converse is not true.  ... 
<span class="external-identifiers"> </span>
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Page 747 of Mathematical Reviews Vol. 51, Issue 3 [page]

<span title="">1976</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The author presents a model-theoretic proof of Riickert’s Null- stellensatz, a problem suggested by A. Robinson [Applications of model theory to algebra, analysis, and probability (Internat.  ...  For one thing, the topological definition of weak forcing, say, in the set- theoretic case, is well-known; the author himself refers to a 1966 source by G.  ... 
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Page 2848 of Mathematical Reviews Vol. , Issue 95e [page]

<span title="">1995</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Given a manifold X with a submanifold F, the Sullivan minimal models of which are related by a deformation in the sense of C. Allday [Topology 17 (1978), no. 1, 95-100; MR 58 #18501].  ...  It can be used as a textbook in a graduate course for students who have some basic training in algebraic topology and differential geometry.  ... 
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Page 3482 of Mathematical Reviews Vol. , Issue 81I [page]

<span title="">1981</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Granting that algebraic topology should be able to deal with homology theories in general, and the result in this paper that A(X) localized to zero is ordinary rational homology theory (7,A °(X)®Q=H,(X  ...  The theoretical framework that produces these results is outlined in the second half of the paper.  ... 
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A note on proximity spaces and connection based mereology

Dimiter Vakarelov, Ivo Düntsch, Brandon Bennett
<span title="">2001</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sfap2xu2qzchzj5ik5e7tblnfe" style="color: black;">Proceedings of the international conference on Formal Ontology in Information Systems - FOIS &#39;01</a> </i> &nbsp;
In this note, we prove a topological representation theorem for a connection based class of systems, using methods and tools from the theory of proximity spaces.  ...  The key novelty is a new proximity semantics for connection relations.  ...  Ivo Düntsch acknowledges a brief discussion with John Stell in 1997 about proximity spaces; however, the topic was not pursued further. References  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/505168.505182">doi:10.1145/505168.505182</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/fois/VakarelovDB01.html">dblp:conf/fois/VakarelovDB01</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/n7jvnk7flrgwrfij2idd6trgzi">fatcat:n7jvnk7flrgwrfij2idd6trgzi</a> </span>
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Preface [chapter]

<span title="2021-08-09">2021</span> <i title="De Gruyter"> Topics in Infinite Group Theory </i> &nbsp;
The first chapter deals with free constructions and one-relator groups. We give a thorough introduction to these topics and accompany our exposition with several applications.  ...  In this sense we put special emphasis on the possibility to prove theorems with different methods: algebraic, topological and geometric.  ...  In particular we have to mention Anja Rosenberger and Annika Schürenberg as well as the many students who have taken part in the respective courses.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/9783110673371-201">doi:10.1515/9783110673371-201</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/23bpgyc56vadpmk7zwq5o73gm4">fatcat:23bpgyc56vadpmk7zwq5o73gm4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211011012024/https://www.degruyter.com/document/doi/10.1515/9783110673371-201/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/b0/a0/b0a0df1168c7f492370ebe8525cd11518027b4d7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/9783110673371-201"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> degruyter.com </button> </a>

Page 654 of Mathematical Reviews Vol. , Issue 88b [page]

<span title="">1988</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
There is no doubt that this is an important and growing area of study, with significant applications in theoretical computer science and related fields.  ...  In this paper a good deal of the theory of these algebras is developed; in partic- ular, a certain case of the word problem is considered, and a result on free subalgebras of a Turing algebra is proved  ... 
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