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Algebraic models for T1-spaces

2011
*
Topology and its Applications
*

These are conditionally up-complete, algebraic

doi:10.1016/j.topol.2011.01.014
fatcat:oqbwz6iu7jcxfpoaubg2ljkayi
*and*maximized*posets*in which every compact element is a meet of maximal elements,*and*they provide*essentially*unique algebraic ordered models for T 1 -base ... Stone duality T 1 -space Zero-dimensional We show that the T 1 -spaces are precisely the maximal point spaces of conditionally upcomplete algebraic*posets*with the Scott*topology*. ... Lemma 1 . 1 In the underlying*poset*of a T 0 -space (with specialization order x y ⇔ x ∈ {y}), meet-*density*of subsets entails*topological**density*. ...##
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Computability in Basic Quantum Mechanics
[article]

2018
*
arXiv
*
pre-print

*continuously*realizable maps between them. ... In terms of the Hilbert lattice L of closed linear subspaces of H the notions of state

*and*observable can be formulated as kinds of measures as in [21]. ... Simpson

*and*B. Spitters for discussions

*and*helpful hints. In particular, we want to thank M. ...

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Trees, Gleason spaces, and coabsolutes of $\beta {\bf N}\sim {\bf N}$

1982
*
Transactions of the American Mathematical Society
*

In §2, we begin an application of §1 to

doi:10.1090/s0002-9947-1982-0648079-x
fatcat:bhbju2ff5batnko74vivmoomgu
*topology*with several theorems. ... We also give (2.6*and*2.7) sufficient conditions (dependent*on*certain cardinal functions) for a space X to have a dense linearly ordered subspace. ... (3.9 ) If A is a locally compact noncompact metric space of*density*at most 2", then A* is coabsolute with*one*of N*, R*, or N* + R*. ...##
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Dualities between finitely separated structures
[article]

2012
*
arXiv
*
pre-print

We study dualities between classes of relational

arXiv:1212.3758v1
fatcat:qvo6lsue6jchnlb2ohmlj4v3l4
*topological*structures, given by Hom-functors. ... We show that there exists a 2-element structure with infinitely many relations, which reconstructs all other structures generated by a 2-element*one*. ... It is moreover*continuous*with respect to the product*topology**on*X * * which is just the*topology*of pointwise convergence. ...##
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The Distributive Full Lambek Calculus with Modal Operators
[article]

2020
*
arXiv
*
pre-print

After that, we establish a Priestley-style duality between residuated distributive modal algebras

arXiv:2003.09975v3
fatcat:rbrz2afsw5fxrifkghudzr3fti
*and**topological*Kripke structures based*on*Priestley spaces. ... We prove that any canonical logic is Kripke complete via discrete duality*and*canonical extensions. ... Let us recall the*essential*facts about (prime) filters*on*bounded distributive residuated lattices, see [15] [49] . ...##
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Wadge-like reducibilities on arbitrary quasi-Polish spaces

2014
*
Mathematical Structures in Computer Science
*

We consider weaker notions of reducibility, including the so-called Δ0α-reductions,

doi:10.1017/s0960129513000339
fatcat:5zxl3cp6sbbjdp4cccjkeccqsu
*and*try to find for various natural*topological*spacesXthe least ordinal αXsuch that for every αX⩽ β < ω1the degree-structure ...*and*its powers. ... the*poset*(ω, ≥) with the Scott (equivalently, the Alexandrov)*topology*. ...##
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Euler characteristics of centralizer subcategories
[article]

2015
*
arXiv
*
pre-print

Let p be a prime number, G a finite group,

arXiv:1502.01317v2
fatcat:jznxy7yorfadhjkc74hagqgqji
*and*A a finite group acting*on*G. The Brown*poset*of nonidentity p-subgroups of G is then an A-*poset*. ... The second equivariant Euler characteristic for the conjugation of G*on*the Brown*poset*for G is especially intriguing because of its relation to the Knorr-Robinson conjecture*and*we carry out a concrete ... By construction, iK is full*and*faithful,*and*as it is also*essentially*surjective*on*objects, iK is an equivalence of categories. ...##
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Viral Vectors I: Major Viral Vectors

2000
*
Molecular Therapy
*

In point-free

doi:10.1006/mthe.2000.0143
fatcat:t7k2ymu7rjeirdh3zhe4cxuxju
*topology*, for a frame L,*one*encounters as a counterpart to C(X) (resp. C * (X)), the well-studied f -ring RL of real-valued*continuous*functions*on*L*and*its bounded part R * L. ... of Coimbra (Portugal) In Pointfree*Topology*, a*continuous*real function*on*a frame L is a map from the frame L(R) of reals into L. ...##
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Stratified computation of skylines with partially-ordered domains

2005
*
Proceedings of the 2005 ACM SIGMOD international conference on Management of data - SIGMOD '05
*

Based

doi:10.1145/1066157.1066181
dblp:conf/sigmod/ChanET05
fatcat:h3dyyijhqzh27ejyif4ayjxv3e
*on*this framework, we propose three novel algorithms: BBS + is a straightforward adaptation of BBS using the framework,*and*SDC (Stratification by Dominance Classification)*and*SDC + are optimized ... Our solution is to transform each partially-ordered attribute into a two-integer domain that allows us to exploit index-based algorithms to compute skyline queries*on*the transformed space. ... The*density*of edges in the*poset*is controlled by the number of iterations of adding inter-tree edges*and*the probability of adding an edge for a node. ...##
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Quantalic spectra of semirings
[article]

2022
*
arXiv
*
pre-print

of a commutative ring, the Gelfand spectrum of a commutative unital C*-algebra

arXiv:2201.06408v1
fatcat:t5lerozdereafjtkldfatcsuyi
*and*the Hofmann-Lawson spectrum of a*continuous*frame. ... We then provide an explicit construction of this spectrum under conditions*on*R which are satisfied by our main examples. ... The ring R = S1 ×*S2*can be obtained as either the ring of R-valued functions*on*the*one*-point space or the ring of sections of the bundle S1 t*S2*→ {1, 2}. ...##
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The Markov-quantile process attached to a family of marginals

2021
*
Journal de l'École polytechnique. Mathématiques
*

Since the measures t ( Lev s1,

doi:10.5802/jep.177
fatcat:kqyywl6d45h6rnunis5fi6bawq
*s2*)*and*Lev*s2*,...,s k have increasing kernel, we have only to show that Lev s1,*s2*. Lev*s2*,s3 = Lev s1,*s2*. L {*s2*} . ... -A sequence (P n ) n of (probability) measures*on*some measurable*topological*space E converges weakly to P if, for all bounded*continuous*function f , f dP n → f dP . ... -Let (µ t ) t∈[0,1] be concentrated*on*N for every t*and*assume that for every k ∈ N the map Examples*and*open questions )*and*piecewise monotone (e.g., A k is analytic). ...##
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Metric Geometry of Finite Subset Spaces
[article]

2021
*
arXiv
*
pre-print

A related question is "If X

arXiv:2004.09419v4
fatcat:ivxffx6sanbxjjkxmujxkywodi
*and*Y have a geometric relation R, does it follow that X(n)*and*Y(n) also have the relation R?". (Truncated) ... ., distance, or length of a path, between points)*on*X. In such a study, we call a space X metrizable if X is homeomorphic to a metric space. ...*On*the other hand, the results of section A.3*on**topological*extension theorems*and*of section A.4*on*metrizability of spaces are not strictly*essential*,*and*so a reader who is familiar with the results ...##
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Sequential Product of Quantum Effects: An Overview

2010
*
International Journal of Theoretical Physics
*

Finally, we prove some new results concerning TEMs

doi:10.1007/s10773-010-0390-6
fatcat:ka3qiypnibhsverlt5ckayaefa
*and*vector*densities*. ... We next treat transition effect matrices (TEMs)*and*their associated sequential product. A TEM is a matrix whose entries are effects*and*whose rows form quantum measurements. ... Then a TEM A*on*E takes every singular vector*density*to a singular vector*density*if*and*only if A is a 0-1 TEM.Proof. ...##
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Equivariant vector bundles on Drinfeld's upper half space

2008
*
Inventiones Mathematicae
*

Schneider for their numerous

doi:10.1007/s00222-008-0112-3
fatcat:as5q4wsitzdani6awcc6apvvte
*and*interesting remarks*on*this paper. Further, I would like to thank Benjamin Schraen for indicating a mistake in a previous version. ... Strauch for pointing out to me the topic treated in this paper*and*for all the discussions we had during our stay at the IHÉS in 2004. I wish to thank M. Rapoport*and*P. ... spaces has the*topological*Mittag-Leffler property by our condition*on*the*density*, cf.[EGAIII] 13.2.4. ...##
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Equivariant vector bundles on Drinfeld's upper half space
[article]

2007
*
arXiv
*
pre-print

This paper generalizes the cases of the canonical bundle due to Schneider

arXiv:math/0606355v3
fatcat:i2y2vvekeveyxersggv6mb7afq
*and*Teitelbaum*and*that of the structure sheaf by Pohlkamp. ... We construct for every homogeneous vector bundle F*on*the projective space P^d a GL_d+1(K)-equivariant filtration by closed K-Frechet spaces*on*F(X). ... Schneider for their numerous*and*interesting remarks*on*this paper. Further, I would like to thank Benjamin Schraen for indicating a mistake in a previous version. ...
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