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Matematicheskie Zametki, 2018, Volume 104, Issue 1, Pages 87–98
DOI: https://doi.org/10.4213/mzm10961 (Mi mzm10961) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The Separability and Sequential Separability of the Space $C(X)$

A. V. Osipovabc

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
c Ural State University of Economics, Ekaterinburg
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DOI: https://doi.org/10.4213/mzm10961
Abstract: The following results are obtained: (1) a criterion for the separability of the space of continuous functions $C(X)$ with the set-open topology; (2) a criterion for the sequential separability of the space $C_{p}(A|X)$, where $A\subseteq X$; (3) an answer to Velichko's question of whether a set-theoretic condition on a metric space $X$ in the criterion for the sequential separability of $C_{p}(X)$ is essential.
Keywords: space of continuous functions, separability, sequential separability, set-open topology.
Received: 19.09.2015
Revised: 18.11.2017
English version:
Mathematical Notes, 2018, Volume 104, Issue 1, Pages 86–95
DOI: https://doi.org/10.1134/S0001434618070106
Bibliographic databases:
Document Type: Article
UDC: 515.122+515.126
Language: Russian
Citation: A. V. Osipov, “The Separability and Sequential Separability of the Space $C(X)$”, Mat. Zametki, 104:1 (2018), 87–98; Math. Notes, 104:1 (2018), 86–95
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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