Selections generating new topologies

被引：5

作者：

Gutev, Valentin

Tomita, Artur

机构：

[1] Univ KwaZulu Natal, Fac Sci, Sch Math Sci, ZA-4041 Durban, South Africa

[2] Univ Sao Paulo, Dept Matemat, Inst Matemat & Estatist, BR-05315970 Sao Paulo, Brazil

来源：

PUBLICACIONS MATEMATIQUES | 2007年 / 51卷 / 01期

关键词：

hyperspace topology; Vietoris topology; continuous selection;

D O I：

10.5565/PUBLMAT_51107_01

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Every (continuous) selection for the non-empty 2-point subsets of a space X naturally defines in interval-like topology on X. In the present paper, we demonstrate that, for a second-countable zero-dimensional space X, this topology may fail to be first-countable at some (or, even any) point of X. This settles some problems stated in [7].

引用

页码：3 / 15

页数：13

共 14 条

[1] Ordered topological spaces [J].