Separability and Sequential Separability of the Space C(X)

被引：0
|
作者：
Osipov, A. V. [1 ,2 ,3 ]
机构：
[1] Russian Acad Sci, Ural Branch, Krasovskii Inst Math & Mech, Ekaterinburg 620990, Russia
[2] Ural Fed Univ, Ekaterinburg 620002, Russia
[3] Ural State Univ Econ, Ekaterinburg 620219, Russia
来源：
MATHEMATICAL NOTES | 2018年 / 104卷 / 1-2期
关键词：
space of continuous functions; separability; sequential separability; set-open topology; DENSITY;
D O I：
10.1134/S0001434618070106
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 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 C-p(X) is necessary.
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页码：86 / 95
页数：10
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