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Mat. Zametki, 2018, Volume 104, Issue 1, Pages 87–98 (Mi mz10961)  

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

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.

DOI: https://doi.org/10.4213/mzm10961

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English version:
Mathematical Notes, 2018, 104:1, 86–95

Bibliographic databases:

UDC: 515.122+515.126
Received: 19.09.2015
Revised: 18.11.2017

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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