Email this article Separability and Sequential Separability of the Space C(X)
- Authors: Osipov A.V.1,2,3
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Affiliations:
- Krasovskii Institute of Mathematics and Mechanics
- Ural Federal University
- Ural State University of Economics
- Issue: Vol 104, No 1-2 (2018)
- Pages: 86-95
- Section: Article
- URL: https://ogarev-online.ru/0001-4346/article/view/151123
- DOI: https://doi.org/10.1134/S0001434618070106
- ID: 151123
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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 Cp(A|X), where A ⊆ X; (3) an answer to Velichko’s question of whether a set-theoretic condition on a metric space X in a criterion for the sequential separability of Cp(X) is necessary.
About the authors
A. V. Osipov
Krasovskii Institute of Mathematics and Mechanics; Ural Federal University; Ural State University of Economics
Author for correspondence.
Email: oab@list.ru
Russian Federation, Yekaterinburg, 620990; Yekaterinburg, 620002; Yekaterinburg, 620219
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