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Some relative properties on normality and paracompactness, and their absolute embeddings

Shinji Kawaguchi, Ryoken Sokei (2005)

Commentationes Mathematicae Universitatis Carolinae

Paracompactness (-paracompactness) and normality of a subspace in a space defined by Arhangel’skii and Genedi [4] are fundamental in the study of relative topological properties ([2], [3]). These notions have been investigated by primary using of the notion of weak - or weak -embeddings, which are extension properties of functions defined in [2] or [18]. In fact, Bella and Yaschenko [8] characterized Tychonoff spaces which are normal in every larger Tychonoff space, and this result is essentially...

The concept of boundedness and the Bohr compactification of a MAP Abelian group

Jorge Galindo, Salvador Hernández (1999)

Fundamenta Mathematicae

Let G be a maximally almost periodic (MAP) Abelian group and let ℬ be a boundedness on G in the sense of Vilenkin. We study the relations between ℬ and the Bohr topology of G for some well known groups with boundedness (G,ℬ). As an application, we prove that the Bohr topology of a topological group which is topologically isomorphic to the direct product of a locally convex space and an -group, contains “many” discrete C-embedded subsets which are C*-embedded in their Bohr compactification. This...

The partially pre-ordered set of compactifications of Cp(X, Y)

A. Dorantes-Aldama, R. Rojas-Hernández, Á. Tamariz-Mascarúa (2015)

Topological Algebra and its Applications

In the set of compactifications of X we consider the partial pre-order defined by (W, h) ≤X (Z, g) if there is a continuous function f : Z ⇢ W, such that (f ∘ g)(x) = h(x) for every x ∈ X. Two elements (W, h) and (Z, g) of K(X) are equivalent, (W, h) ≡X (Z, g), if there is a homeomorphism h : W ! Z such that (f ∘ g)(x) = h(x) for every x ∈ X. We denote by K(X) the upper semilattice of classes of equivalence of compactifications of X defined by ≤X and ≡X. We analyze in this article K(Cp(X, Y)) where...

The Rothberger property on

Daniel Bernal-Santos (2016)

Commentationes Mathematicae Universitatis Carolinae

A space is said to have the Rothberger property (or simply is Rothberger) if for every sequence of open covers of , there exists for each such that . For any , necessary and sufficient conditions are obtained for to have the Rothberger property when is a Mrówka mad family and, assuming CH (the Continuum Hypothesis), we prove the existence of a maximal almost disjoint family for which the space is Rothberger for all .

The subspace of weak -points of

Salvador García-Ferreira, Y. F. Ortiz-Castillo (2015)

Commentationes Mathematicae Universitatis Carolinae

Let be the subspace of consisting of all weak -points. It is not hard to see that is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that is a -pseudocompact space for all .

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