Dense families of selections and finite-dimensional spaces

被引：10

作者：

Gutev, V

Valov, V

机构：

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

[2] Nipissing Univ, Dept Math & Comp Sci, N Bay, ON P1B 8L7, Canada

来源：

SET-VALUED ANALYSIS | 2003年 / 11卷 / 04期

关键词：

continuous selection; finite-dimensional space; strongly countable-dimensional space; Zn-set;

D O I：

10.1023/A:1025679902969

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A characterization of n-dimensional spaces via continuous selections avoiding Z(n)-sets is given, and a selection theorem for strongly countable-dimensional spaces is established. We apply these results to prove a generalized Ostrand's theorem, and to obtain a new alternative proof of the Hurewicz formula. It is also shown that our selection theorem yields an easy proof of a Michael's result.

引用

页码：373 / 391

页数：19