Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/101593
Title: On selective sequential separability of function spaces with the compact-open topology
Authors: Osipov, A. V.
Issue Date: 2019
Publisher: Hacettepe University
Citation: Osipov A. V. On selective sequential separability of function spaces with the compact-open topology / A. V. Osipov. — DOI 10.15672/HJMS.2018.635 // Hacettepe Journal of Mathematics and Statistics. — 2019. — Vol. 48. — Iss. 6. — P. 1761-1766.
Abstract: For a Tychonoff space X, we denote by Ck (X) the space of all real-valued continuous functions on X with the compact-open topology. A subset A ⊂ X is said to be sequentially dense in X if every point of X is the limit of a convergent sequence in A. A space Ck (X) is selectively sequentially separable (in Scheepers’ terminology: Ck (X) satisfies Sfin(S, S)) if whenever (Sn: n ∈ N) is a sequence of sequentially dense subsets of Ck (X), one can pick finite Fn ⊂ Sn (n ∈ N) such that∪ {Fn: n ∈ N} is sequentially dense in Ck (X). In this paper, we give a characterization for Ck (X) to satisfy Sfin(S, S). © 2019, Hacettepe University. All rights reserved.
Keywords: COMPACT-OPEN TOPOLOGY
FUNCTION SPACE
PROPERTY Α2
PROPERTY Α4
S1(S,S)
SELECTIVELY SEQUENTIALLY SEPARABLE
SEQUENTIALLY DENSE SET
URI: http://hdl.handle.net/10995/101593
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85077523515
PURE ID: 11900979
09f9d4d2-8975-49dd-8e87-6b18a424dc09
ISSN: 2651477X
DOI: 10.15672/HJMS.2018.635
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