Finite-to-one continuous s-covering mappings

Alexey Ostrovsky

Displaying similar documents to “Finite-to-one continuous s-covering mappings”

Monotonically normal $e$ -separable spaces may not be perfect

John E. Porter (2018)

Commentationes Mathematicae Universitatis Carolinae

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A topological space $X$ is said to be $e$ -separable if $X$ has a $σ$ -closed-discrete dense subset. Recently, G. Gruenhage and D. Lutzer showed that $e$ -separable PIGO spaces are perfect and asked if $e$ -separable monotonically normal spaces are perfect in general. The main purpose of this article is to provide examples of $e$ -separable monotonically normal spaces which are not perfect. Extremely normal $e$ -separable spaces are shown to be stratifiable.

$F_{σ}$ -mappings and the invariance of absolute Borel classes

Petr Holický, Jiří Spurný (2004)

Fundamenta Mathematicae

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It is proved that $F_{σ}$ -mappings preserve absolute Borel classes, which improves results of R. W. Hansell, J. E. Jayne and C. A. Rogers. The proof is based on the fact that any $F_{σ}$ -mapping f: X → Y of an absolute Suslin metric space X onto an absolute Suslin metric space Y becomes a piecewise perfect mapping when restricted to a suitable $F_{σ}$ -set $X_{\infty} \subset X$ satisfying $f (X_{\infty}) = Y$ .

Less than $2^{ω}$ many translates of a compact nullset may cover the real line

Márton Elekes, Juris Steprāns (2004)

Fundamenta Mathematicae

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We answer a question of Darji and Keleti by proving that there exists a compact set C₀ ⊂ ℝ of measure zero such that for every perfect set P ⊂ ℝ there exists x ∈ ℝ such that (C₀+x) ∩ P is uncountable. Using this C₀ we answer a question of Gruenhage by showing that it is consistent with ZFC (as it follows e.g. from $c o f () < 2^{ω}$ ) that less than $2^{ω}$ many translates of a compact set of measure zero can cover ℝ.

On decomposability of finite groups

Ruifang Chen, Xianhe Zhao (2017)

Czechoslovak Mathematical Journal

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Let $G$ be a finite group. A normal subgroup $N$ of $G$ is a union of several $G$ -conjugacy classes, and it is called $n$ -decomposable in $G$ if it is a union of $n$ distinct $G$ -conjugacy classes. In this paper, we first classify finite non-perfect groups satisfying the condition that the numbers of conjugacy classes contained in its non-trivial normal subgroups are two consecutive positive integers, and we later prove that there is no non-perfect group such that the numbers of conjugacy classes contained...

A note on star Lindelöf, first countable and normal spaces

Wei-Feng Xuan (2017)

Mathematica Bohemica

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A topological space $X$ is said to be star Lindelöf if for any open cover $𝒰$ of $X$ there is a Lindelöf subspace $A \subset X$ such that $St (A, 𝒰) = X$ . The “extent” $e (X)$ of $X$ is the supremum of the cardinalities of closed discrete subsets of $X$ . We prove that under $V = L$ every star Lindelöf, first countable and normal space must have countable extent. We also obtain an example under $MA + \neg CH$ , which shows that a star Lindelöf, first countable and normal space may not have countable extent.

A new Lindelöf space with points $G_{δ}$

Alan S. Dow (2015)

Commentationes Mathematicae Universitatis Carolinae

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We prove that $♦^{*}$ implies there is a zero-dimensional Hausdorff Lindelöf space of cardinality $2^{ℵ_{1}}$ which has points $G_{δ}$ . In addition, this space has the property that it need not be Lindelöf after countably closed forcing.

Characterizations of $z$ -Lindelöf spaces

Ahmad Al-Omari, Takashi Noiri (2017)

Archivum Mathematicum

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A topological space $(X, τ)$ is said to be $z$ -Lindelöf [1] if every cover of $X$ by cozero sets of $(X, τ)$ admits a countable subcover. In this paper, we obtain new characterizations and preservation theorems of $z$ -Lindelöf spaces.

A note on spaces with countable extent

Yan-Kui Song (2017)

Commentationes Mathematicae Universitatis Carolinae

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Let $P$ be a topological property. A space $X$ is said to be star P if whenever $𝒰$ is an open cover of $X$ , there exists a subspace $A \subseteq X$ with property $P$ such that $X = S t (A, 𝒰)$ . In this note, we construct a Tychonoff pseudocompact SCE-space which is not star Lindelöf, which gives a negative answer to a question of Rojas-Sánchez and Tamariz-Mascarúa.

Possibly there is no uniformly completely Ramsey null set of size $2^{ω}$

Andrzej Nowik (2002)

Colloquium Mathematicae

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We show that under the axiom $C P A_{c u b e}$ there is no uniformly completely Ramsey null set of size $2^{ω}$ . In particular, this holds in the iterated perfect set model. This answers a question of U. Darji.

A characterization of complex $L_{1}$ -preduals via a complex barycentric mapping

Petr Petráček, Jiří Spurný (2016)

Commentationes Mathematicae Universitatis Carolinae

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We provide a complex version of a theorem due to Bednar and Lacey characterizing real $L_{1}$ -preduals. Hence we prove a characterization of complex $L_{1}$ -preduals via a complex barycentric mapping.

Spaces with star countable extent

A. D. Rojas-Sánchez, Angel Tamariz-Mascarúa (2016)

Commentationes Mathematicae Universitatis Carolinae

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For a topological property $P$ , we say that a space $X$ is star $P$ if for every open cover $𝒰$ of the space $X$ there exists $A \subset X$ such that $s t (A, 𝒰) = X$ . We consider space with star countable extent establishing the relations between the star countable extent property and the properties star Lindelöf and feebly Lindelöf. We describe some classes of spaces in which the star countable extent property is equivalent to either the Lindelöf property or separability. An example is given of a Tychonoff star Lindelöf...