Locally compact path spaces

被引：0

作者：

Niefield, SB ^{[1
]}

机构：

[1] Union Coll, Schenectady, NY 12308 USA

来源：

APPLIED CATEGORICAL STRUCTURES | 2005年 / 13卷 / 01期

关键词：

locally compact; compact-open topology; path space;

D O I：

10.1007/s10485-004-5012-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that the space X-[0,X-1], of continuous maps [0, 1] --> X with the compact-open topology, is not locally compact for any space X having a nonconstant path of closed points. For a T-1-space X, it follows that X-[0,X-1] is locally compact if and only if X is locally compact and totally path-disconnected.

引用

页码：65 / 69

页数：5

共 13 条

[1]

[Anonymous], 1955, GRADUATE TEXTS MATH

[2]

DAY BJ, 1970, PROC CAMB PHILOS S-M, V67, P553

[3] ON TOPOLOGIES FOR FUNCTION SPACES [J].