If Cp(X) is strongly dominated by a second countable space, then X is countable

被引：12

作者：

Guerrero Sanchez, D. ^{[1
]}

Tkachuk, V. V. ^{[1
]}

机构：

[1] Univ Autonoma Metropolitana, Dept Matemat, Ave San Rafael Atlixco,186,Col Vicentina, Mexico City 09340, DF, Mexico

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 454卷 / 02期

关键词：

Domination; Strong domination; Compact space; Second countable space; Function space; The space of the irrationals;

D O I：

10.1016/j.jmaa.2017.05.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish that a Tychonoff space X is countable if and only if C-p(X) is strongly dominated by a second countable space. The same is true for a compact space K such that C-p(K, [0,1]) is strongly dominated by a second countable space. We also prove that strong domination by a second countable space of the complement of the diagonal of a Tychonoff space X implies that X is an N-0-space. Our results solve several published open questions. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：533 / 541

页数：9

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