Results 51 to 60 of about 560 (152)
On RG-spaces and the regularity degree
Applied General Topology, 2006 We continue the study of a lattice-ordered ring G(X), associated with the ring C(X). Following, X is called RG when G(X) = C(Xδ). An RG-space must have a dense set of very weak P-points.
R. Raphael, R.G. Woods
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On complemented copies of the space c0 in spaces Cp(X,E)$C_p(X,E)$
Mathematische Nachrichten, Volume 297, Issue 2, Page 644-656, February 2024.Abstract We study the question for which Tychonoff spaces X and locally convex spaces E the space Cp(X,E)$C_p(X,E)$ of continuous E‐valued functions on X contains a complemented copy of the space (c0)p={x∈Rω:x(n)→0}$(c_0)_p=\lbrace x\in \mathbb {R}^\omega : x(n)\rightarrow 0\rbrace$, both endowed with the pointwise topology.
Christian Bargetz +2 more
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Unions of chains of subgroups of a topologucal group
Applied General Topology, 2001 We consider the following problem: If a topological group G is the union of an increasing chain of subgroups and certain cardinal invariants of the subgroups in the chain are known, what can be said about G?
Yolanda Torres Falcón
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Outer measures associated with lattice measures and their application
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 4, Page 725-734, 1995., 1994 Consider a set X and a lattice ℒ of subsets of X such that ϕ, X ∈ ℒ. M(ℒ) denotes those bounded finitely additive measures on A(ℒ) which are studied, and I(ℒ) denotes those elements of M(ℒ) which are 0 − 1 valued. Associated with a μ ∈ M(ℒ) or a μ ∈ Mσ(ℒ) (the elements of M(ℒ) which are σ‐smooth on ℒ) are outer measures μ′ and μ″.
Charles Traina
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Pseudocompact totally dense subgroups [PDF]
, 2008 It was shown by Dikranjan and Shakhmatov in 1992 that if a compact abelian group K admits a proper totally dense pseudocompact subgroup, then K cannot have a torsion closed G_delta-subgroup; moreover this condition was shown to be also sufficient under ...
DIKRANJAN, Dikran, GIORDANO BRUNO, Anna
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The equivalence of two definitions of sequential pseudocompactness
Applied General Topology, 2016 We show that two possible definitions of sequential pseudocompactness are equivalent, and point out some consequences.
Paolo Lipparini
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On pseudocompactness and related notions in ZF [PDF]
Commentationes Mathematicae Universitatis Carolinae, 2018 It is well-known that some topological properties and implications/non-implications among them are closely related with certain set theories. Let ZF denote the Zermelo-Fraenkel set theory and let ZFC be the set theory ZF together with the axiom of choice AC.
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Making group topologies with, and without, convergent sequences
Applied General Topology, 2006 (1) Every infinite, Abelian compact (Hausdorff) group K admits 2|K|- many dense, non-Haar-measurable subgroups of cardinality |K|. When K is nonmetrizable, these may be chosen to be pseudocompact. (2) Every infinite Abelian group G admits a family A of
W.W. Comfort +2 more
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New characterisations of pseudocompact spaces [PDF]
Bulletin of the Australian Mathematical Society, 1988 In this paper, we give a new characterisation of pseudo-compact spaces, namely a space X is pseudocompact if and only if each σ-point finite open cover of X has a finite subfamily whose union is dense. As a corollary, we show that every pseudocompact σ-metacompact (or screenable) space is compact, which sharpens some known results.
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Some results and problems about weakly pseudocompact spaces [PDF]
, 2000 summary:A space $X$ is {\it truly weakly pseudocompact} if $X$ is either weakly pseudocompact or Lindelöf locally compact. We prove: (1) every locally weakly pseudocompact space is truly weakly pseudocompact if it is either a generalized linearly ordered
Tamariz-Mascarúa, Angel, Okunev, Oleg
core