Results 1 to 10 of about 47 (47)
Applied General Topology, 2021 Let C∞ (X) denote the family of real-valued continuous functions which vanish at infinity in the sense that {x ∈ X : |f(x)| ≥ 1/n} is compact in X for all n ∈ N. It is not in general true that C∞ (X) is an ideal of C(X).
Biswajit Mitra, Debojyoti Chowdhury
doaj +1 more source
Pseudocompact and precompact topological subsemigroups of topological groups
Pracì Mìžnarodnogo Geometričnogo Centru, 2023 It is known that every pseudocompact topological group is precompact, we extend this result to a class of subsemigroup of topological groups. Then we use this results to prove that cancellative locally compact countably compact topological semigroups ...
Julio Cesar Hernandez
doaj +1 more source
Weakly metrizable pseudocompact groups
Applied General Topology, 2006 We study various weaker versions of metrizability for pseudocompact abelian groups G: singularity (G possesses a compact metrizable subgroup of the form mG, m > 0), almost connectedness (G is metrizable modulo the connected component) and various ...
Dikran Dikranjan +2 more
doaj +1 more source
Few remarks on maximal pseudocompactness
Applied General Topology, 2018 A pseudocompact space is maximal pseudocompact if every strictly finer topology is no longer pseudocompact. The main result here is a counterexample which answers a question rised by Alas, Sanchis and Wilson.
Angelo Bella
doaj +1 more source
Non-Abelian Pseudocompact Groups
Axioms, 2016 Here are three recently-established theorems from the literature. (A) (2006) Every non-metrizable compact abelian group K has 2|K| -many proper dense pseudocompact subgroups.
W. W. Comfort, Dieter Remus
doaj +1 more source
Selectively Pseudocompact Groups without Infinite Separable Pseudocompact Subsets
Axioms, 2018 We give a “naive” (i.e., using no additional set-theoretic assumptions beyond ZFC, the Zermelo-Fraenkel axioms of set theory augmented by the Axiom of Choice) example of a Boolean topological group G without infinite separable pseudocompact subsets ...
Dmitri Shakhmatov, Víctor Hugo Yañez
doaj +1 more source
Applied General Topology, 2015 Suppose $F$ is a totally ordered field equipped with its order topology and $X$ a completely $F$-regular topological space. Suppose $\mathcal{P}$ is an ideal of closed sets in $X$ and $X$ is locally-$\mathcal{P}$.
Sudip Kumar Acharyya +2 more
doaj +1 more source
Closed subsets of compact-like topological spaces
Applied General Topology, 2020 We investigate closed subsets (subsemigroups, resp.) of compact-like topological spaces (semigroups, resp.). We show that each Hausdorff topological space is a closed subspace of some Hausdorff ω-bounded pracompact topological space and describe open ...
Serhii Bardyla, Alex Ravsky
doaj +1 more source
A note on weakly pseudocompact locales
Applied General Topology, 2017 We revisit weak pseudocompactness in pointfree topology, and show that a locale is weakly pseudocompact if and only if it is Gδ-dense in some compactification.
Themba Dube
doaj +1 more source
Intermediate rings of complex-valued continuous functions
Applied General Topology, 2021 For a completely regular Hausdorff topological space X, let C(X, C) be the ring of complex-valued continuous functions on X, let C ∗ (X, C) be its subring of bounded functions, and let Σ(X, C) denote the collection of all the rings that lie between C ...
Amrita Acharyya +3 more
doaj +1 more source