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Mapping theorems on countable tightness and a question of F. Siwiec

Shou Lin, Jinhuang Zhang (2014)

Commentationes Mathematicae Universitatis Carolinae

In this paper s s -quotient maps and s s q -spaces are introduced. It is shown that (1) countable tightness is characterized by s s -quotient maps and quotient maps; (2) a space has countable tightness if and only if it is a countably bi-quotient image of a locally countable space, which gives an answer for a question posed by F. Siwiec in 1975; (3) s s q -spaces are characterized as the s s -quotient images of metric spaces; (4) assuming 2 ω < 2 ω 1 , a compact T 2 -space is an s s q -space if and only if every countably compact subset...

Martin’s Axiom and ω -resolvability of Baire spaces

Fidel Casarrubias-Segura, Fernando Hernández-Hernández, Angel Tamariz-Mascarúa (2010)

Commentationes Mathematicae Universitatis Carolinae

We prove that, assuming MA, every crowded T 0 space X is ω -resolvable if it satisfies one of the following properties: (1) it contains a π -network of cardinality < 𝔠 constituted by infinite sets, (2) χ ( X ) < 𝔠 , (3) X is a T 2 Baire space and c ( X ) 0 and (4) X is a T 1 Baire space and has a network 𝒩 with cardinality < 𝔠 and such that the collection of the finite elements in it constitutes a σ -locally finite family. Furthermore, we prove that the existence of a T 1 Baire irresolvable space is equivalent to the existence of...

Maximal nowhere dense P -sets in basically disconnected spaces and F -spaces

Andrey V. Koldunov, Aleksandr I. Veksler (2001)

Commentationes Mathematicae Universitatis Carolinae

In [5] the following question was put: are there any maximal n.d. sets in ω * ? Already in [9] the negative answer (under MA) to this question was obtained. Moreover, in [9] it was shown that no P -set can be maximal n.d. In the present paper the notion of a maximal n.d. P -set is introduced and it is proved that under CH there is no such a set in ω * . The main results are Theorem 1.10 and especially Theorem 2.7(ii) (with Example in Section 3) in which the problem of the existence of maximal n.d. P -sets...

Maximal pseudocompact spaces and the Preiss-Simon property

Ofelia Alas, Vladimir Tkachuk, Richard Wilson (2014)

Open Mathematics

We study maximal pseudocompact spaces calling them also MP-spaces. We show that the product of a maximal pseudocompact space and a countable compact space is maximal pseudocompact. If X is hereditarily maximal pseudocompact then X × Y is hereditarily maximal pseudocompact for any first countable compact space Y. It turns out that hereditary maximal pseudocompactness coincides with the Preiss-Simon property in countably compact spaces. In compact spaces, hereditary MP-property is invariant under...

Mazur spaces.

Wilansky, Albert (1981)

International Journal of Mathematics and Mathematical Sciences

Means on scattered compacta

T. Banakh, R. Bonnet, W. Kubis (2014)

Topological Algebra and its Applications

We prove that a separable Hausdor_ topological space X containing a cocountable subset homeomorphic to [0, ω1] admits no separately continuous mean operation and no diagonally continuous n-mean for n ≥ 2.

Measures on Corson compact spaces

Kenneth Kunen, Jan van Mill (1995)

Fundamenta Mathematicae

We prove that the statement: "there is a Corson compact space with a non-separable Radon measure" is equivalent to a number of natural statements in set theory.

Measure-Theoretic Characterizations of Certain Topological Properties

David Buhagiar, Emmanuel Chetcuti, Anatolij Dvurečenskij (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

It is shown that Čech completeness, ultracompleteness and local compactness can be defined by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non-empty support. This shows that these three topological properties are measurable, similarly to the classical examples of compact spaces, pseudo-compact spaces and realcompact spaces.

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