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Algebraic models for T1-spaces

Marcel Erné
2011 Topology and its Applications  
These are conditionally up-complete, algebraic 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.  ... 
doi:10.1016/j.topol.2011.01.014 fatcat:oqbwz6iu7jcxfpoaubg2ljkayi

Computability in Basic Quantum Mechanics [article]

Eike Neumann, Martin Pape, Thomas Streicher
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.  ... 
arXiv:1610.09209v7 fatcat:7fsvrowjg5fizop5hgewlzubsu

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

Scott W. Williams
1982 Transactions of the American Mathematical Society  
In §2, we begin an application of §1 to 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*.  ... 
doi:10.1090/s0002-9947-1982-0648079-x fatcat:bhbju2ff5batnko74vivmoomgu

Dualities between finitely separated structures [article]

Wiesław Kubiś, Krzysztof Pszczoła
2012 arXiv   pre-print
We study dualities between classes of relational 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.  ... 
arXiv:1212.3758v1 fatcat:qvo6lsue6jchnlb2ohmlj4v3l4

The Distributive Full Lambek Calculus with Modal Operators [article]

Daniel Rogozin
2020 arXiv   pre-print
After that, we establish a Priestley-style duality between residuated distributive modal algebras 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] .  ... 
arXiv:2003.09975v3 fatcat:rbrz2afsw5fxrifkghudzr3fti

Wadge-like reducibilities on arbitrary quasi-Polish spaces

LUCA MOTTO ROS, PHILIPP SCHLICHT, VICTOR SELIVANOV
2014 Mathematical Structures in Computer Science  
We consider weaker notions of reducibility, including the so-called Δ0α-reductions, 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.  ... 
doi:10.1017/s0960129513000339 fatcat:5zxl3cp6sbbjdp4cccjkeccqsu

Euler characteristics of centralizer subcategories [article]

Jesper M. Møller
2015 arXiv   pre-print
Let p be a prime number, G a finite group, 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.  ... 
arXiv:1502.01317v2 fatcat:jznxy7yorfadhjkc74hagqgqji

Viral Vectors I: Major Viral Vectors

2000 Molecular Therapy  
In point-free 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.  ... 
doi:10.1006/mthe.2000.0143 fatcat:t7k2ymu7rjeirdh3zhe4cxuxju

Stratified computation of skylines with partially-ordered domains

Chee-Yong Chan, Pin-Kwang Eng, Kian-Lee Tan
2005 Proceedings of the 2005 ACM SIGMOD international conference on Management of data - SIGMOD '05  
Based 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.  ... 
doi:10.1145/1066157.1066181 dblp:conf/sigmod/ChanET05 fatcat:h3dyyijhqzh27ejyif4ayjxv3e

Quantalic spectra of semirings [article]

Graham Manuell
2022 arXiv   pre-print
of a commutative ring, the Gelfand spectrum of a commutative unital C*-algebra 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}.  ... 
arXiv:2201.06408v1 fatcat:t5lerozdereafjtkldfatcsuyi

The Markov-quantile process attached to a family of marginals

Charles Boubel, Nicolas Juillet
2021 Journal de l'École polytechnique. Mathématiques  
Since the measures t ( Lev s1,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).  ... 
doi:10.5802/jep.177 fatcat:kqyywl6d45h6rnunis5fi6bawq

Metric Geometry of Finite Subset Spaces [article]

Earnest Akofor
2021 arXiv   pre-print
A related question is "If X 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  ... 
arXiv:2004.09419v4 fatcat:ivxffx6sanbxjjkxmujxkywodi

Sequential Product of Quantum Effects: An Overview

Stan Gudder
2010 International Journal of Theoretical Physics  
Finally, we prove some new results concerning TEMs 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.  ... 
doi:10.1007/s10773-010-0390-6 fatcat:ka3qiypnibhsverlt5ckayaefa

Equivariant vector bundles on Drinfeld's upper half space

Sascha Orlik
2008 Inventiones Mathematicae  
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.  ...  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.  ... 
doi:10.1007/s00222-008-0112-3 fatcat:as5q4wsitzdani6awcc6apvvte

Equivariant vector bundles on Drinfeld's upper half space [article]

Sascha Orlik
2007 arXiv   pre-print
This paper generalizes the cases of the canonical bundle due to Schneider 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.  ... 
arXiv:math/0606355v3 fatcat:i2y2vvekeveyxersggv6mb7afq
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