Results 1 to 10 of about 33,620 (82)
Precompact Apartness Spaces [PDF]
Logical Methods in Computer Science, 2012 We present a notion of precompactness, and study some of its properties, in the context of apartness spaces whose apartness structure is not necessarily induced by any uniform one. The presentation lies entirely with a Bishop-style constructive framework,
Douglas S Bridges
doaj +1 more source
A few characterizations of topological spaces with no infinite discrete subspace [PDF]
, 2023 We give several characteristic properties of FAC spaces, namely topological spaces with no infinite discrete subspace. The first one was obtained in 2019 by the first author, and states that every closed set is a finite union of irreducible closed ...
Goubault-Larrecq, Jean, Pouzet, Maurice
core +1 more source
Selection principles in mathematics: A milestone of open problems [PDF]
, 2003 We survey some of the major open problems involving selection principles, diagonalizations, and covering properties in topology and infinite combinatorics.
Tsaban, Boaz
core +5 more sources
Coarse amenability and discreteness [PDF]
, 2015 This paper is devoted to dualization of paracompactness to the coarse category via the concept of $R$-disjointness. Property A of G.Yu can be seen as a coarse variant of amenability via partitions of unity and leads to a dualization of paracompactness ...
Dydak, Jerzy
core +1 more source
A semifilter approach to selection principles II: tau*-covers [PDF]
, 2005 In this paper we settle all questions whether (it is consistent that) the properties P and Q [do not] coincide, where P and Q run over selection principles of the type U_fin(O,A).Comment: 9 pages; Latex2e; 1 table; Submitted to ...
Zdomskyy, Lyubomyr
core +4 more sources
Some new directions in infinite-combinatorial topology
, 2006 We give a light introduction to selection principles in topology, a young subfield of infinite-combinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are stated.
A.V. Arkhangel’skii +50 more
core +1 more source
On functional tightness of infinite products
, 2017 A classical theorem of Malykhin says that if $\{X_\alpha:\alpha\leq\kappa\}$ is a family of compact spaces such that $t(X_\alpha)\leq \kappa$, for every $\alpha\leq\kappa$, then $t\left( \prod_{\alpha\leq \kappa} X_\alpha \right)\leq \kappa$, where $t(X)$
Krupski, Mikołaj
core +1 more source
Metrization criteria for compact groups in terms of their dense subgroups
, 2011 According to Comfort, Raczkowski and Trigos-Arrieta, a dense subgroup D of a compact abelian group G determines G if the restriction homomorphism G^ --> D^ of the dual groups is a topological isomorphism.
Dikranjan, Dikran, Shakhmatov, Dmitri
core +1 more source
Compactifications of topological groups [PDF]
, 2001 Every topological group $G$ has some natural compactifications which can be a useful tool of studying $G$. We discuss the following constructions: (1) the greatest ambit $S(G)$ is the compactification corresponding to the algebra of all right uniformly ...
Uspenskij, Vladimir
core +1 more source
Valdivia compact Abelian groups
, 2007 Let R denote the smallest class of compact spaces containing all metric compacta and closed under limits of continuous inverse sequences of retractions. Class R is striclty larger than the class of Valdivia compact spaces.
Kubiś, Wieslaw
core +3 more sources