Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/101750
Title: The Menger and projective Menger properties of function spaces with the set-open topology
Authors: Osipov, A. V.
Issue Date: 2019
Publisher: De Gruyter
Citation: Osipov A. V. The Menger and projective Menger properties of function spaces with the set-open topology / A. V. Osipov. — DOI 10.1515/ms-2017-0258 // Mathematica Slovaca. — 2019. — Vol. 69. — Iss. 3. — P. 699-706.
Abstract: For a Tychonoff space X and a family λ of subsets of X, we denote by Cλ(X) the space of all real-valued continuous functions on X with the set-open topology. A Menger space is a topological space in which for every sequence of open covers u1, u2, ⋯ of the space there are finite sets F1 ? u1, F2 ? u2, ⋯ such that family F1 ∪ F2 ∪ ⋯ covers the space. In this paper, we study the Menger and projective Menger properties of a Hausdorff space Cλ(X). Our main results state that Cλ(X) is Menger if and only if Cλ(X) is σ-compact; Cp(Y | X) is projective Menger if and only if Cp(Y | X) is σ-pseudocompact where Y is a dense subset of X. © 2019 Mathematical Institute Slovak Academy of Sciences.
Keywords: BASICALLY DISCONNECTED SPACE
FUNCTION SPACE
MENGER
PROJECTIVE MENGER
SET-OPEN TOPOLOGY
Σ-BOUNDED
Σ-COMPACT
Σ-PSEUDOCOMPACT
URI: http://hdl.handle.net/10995/101750
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85066866255
PURE ID: 9827578
ISSN: 1399918
DOI: 10.1515/ms-2017-0258
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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