Domination by a Polish space of the complement of the diagonal of X implies that X is cosmic

被引：6

作者：

Guerrero Sanchez, David ^{[1
]}

Tkachuk, Vladimir V. ^{[1
]}

机构：

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

来源：

TOPOLOGY AND ITS APPLICATIONS | 2016年 / 212卷

关键词：

Domination; Compact space; Second countable space; Metrizability; The space P of irrationals; M-diagonal; Cosmic space; Tychonoff cube; COMPACT SPACES;

D O I：

10.1016/j.topol.2016.09.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We will prove that a Tychonoff space X is analytic if and only if (X x X)\Delta is dominated by a Polish space; here Delta = {(x, x) : x is an element of X} is the diagonal of X. This solves two published open questions. We will also establish under CH, that a Tychonoff space X has a countable network whenever (X x X)\Delta is dominated by a second countable space. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：81 / 89

页数：9

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