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We define Peano covering maps and prove basic properties analogous to classical covers. Their domain is always locally path-connected but the range may be an arbitrary topological space. One of characterizations of Peano covering maps is via the uniqueness of homotopy lifting property for all locally path-connected spaces. Regular Peano covering maps over path-connected spaces are shown to be identical with generalized regular covering maps introduced by Fischer and Zastrow....

Covering of a space by nowhere dense sets

Petr Simon (1977)

Commentationes Mathematicae Universitatis Carolinae

Covering properties and product spaces

Telgársky, R. (1972)

General Topology and its Relations to Modern Analysis and Algebra

Covering properties for $L Q 𝒰$ s with nested bases.

Andrikopoulos, A., Stabakis, J.N. (2001)

International Journal of Mathematics and Mathematical Sciences

Covering properties in countable products, II

Sachio Higuchi, Hidenori Tanaka (2006)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we discuss covering properties in countable products of Čech-scattered spaces and prove the following: (1) If $Y$ is a perfect subparacompact space and ${X_{n} : n \in ω}$ is a countable collection of subparacompact Čech-scattered spaces, then the product $Y \times \prod_{n \in ω} X_{n}$ is subparacompact and (2) If ${X_{n} : n \in ω}$ is a countable collection of metacompact Čech-scattered spaces, then the product $\prod_{n \in ω} X_{n}$ is metacompact.

Covering Properties of Continua and Mappings

Janusz J. Charatonik (2003)

Publications de l'Institut Mathématique

Covering space theory for directed topology.

Goubault, Eric, Haucourt, Emmanuel, Krishnan, Sanjeevi (2009)

Theory and Applications of Categories [electronic only]

Covering $Σ_{ξ}^{0}$ -generated ideals by $Π_{ξ}^{0}$ sets

Tamás Mátrai (2007)

Commentationes Mathematicae Universitatis Carolinae

We develop the theory of topological Hurewicz test pairs: a concept which allows us to distinguish the classes of the Borel hierarchy by Baire category in a suitable topology. As an application we show that for every $Π_{ξ}^{0}$ and not $Σ_{ξ}^{0}$ subset $P$ of a Polish space $X$ there is a $σ$ -ideal $ℐ \subseteq 2^{X}$ such that $P \notin ℐ$ but for every $Σ_{ξ}^{0}$ set $B \subseteq P$ there is a $Π_{ξ}^{0}$ set $B^{'} \subseteq P$ satisfying $B \subseteq B^{'} \in ℐ$ . We also discuss several other results and problems related to ideal generation and Hurewicz test pairs.

Covering $^{ω} ω$ by special Cantor sets.

Gruenhage, Gary, Levy, Ronnie (2004)

Commentationes Mathematicae Universitatis Carolinae

Covering $^{ω} ω$ by special Cantor sets

Gary Gruenhage, Ronnie Levy (2002)

Commentationes Mathematicae Universitatis Carolinae

This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space $^{ω} ω$ of irrationals, or certain of its subspaces. In particular, given $f \in^{ω} (ω ∖ {0})$ , we consider compact sets of the form $\prod_{i \in ω} B_{i}$ , where $| B_{i} | = f (i)$ for all, or for infinitely many, $i$ . We also consider “ $n$ -splitting” compact sets, i.e., compact sets $K$ such that for any $f \in K$ and $i \in ω$ , $| {g (i) : g \in K, g ↾ i = f ↾ i} | = n$ .

Coverings by closed sets

Nadler, Sam B. jr. (1967)

Portugaliae mathematica

Cozero and Baire maps on products of uniform spaces

Gloria Tashjian (1977)

Fundamenta Mathematicae

Cp-movable at infinity spaces, compact ANR divisors and property UVWn.

Z. Cerin (1978)

Publications de l'Institut Mathématique [Elektronische Ressource]

Criteria for Eberlein Compactness in Spaces of Continuous Functions.

Dietrich Helmer (1981)

Manuscripta mathematica

Criteria of openness for relations

Marek Wilhelm (1981)

Fundamenta Mathematicae

Criterion of Normality of the Completely Regular Topology of Separate Continuity

Grinshpon, Yakov S. (2006)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 54C10, 54D15, 54G12.For given completely regular topological spaces X and Y, there is a completely regular space X ~⊗ Y such that for any completely regular space Z a mapping f : X × Y ⊗ Z is separately continuous if and only if f : X ~⊗ Y→ Z is continuous. We prove a necessary condition of normality, a sufficient condition of collectionwise normality, and a criterion of normality of the products X ~⊗ Y in the case when at least one factor is scattered.

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