Compactly generated rectifiable spaces or paratopological groups

被引：0

作者：

Lin, Fucai ^{[1
]}

机构：

[1] Minnan Normal Univ, Sch Math & Stat, Zhangzhou 363000, Peoples R China

来源：

MATHEMATICAL COMMUNICATIONS | 2013年 / 18卷 / 02期

关键词：

compactly generated; rectifiable spaces; paratopological groups; sigma-compact; perfect mappings; finitely generated modulo open sets; compactifications; metrizable spaces; quasi-G(delta)-diagonal;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A rectifiable space (or a paratopological group) G is compactly generated if G = < K > for some compact subset K of G. In this paper, we mainly discuss compactly generated rectifiable spaces or paratopological groups. The main results are that: (1) each sigma-compact metrizable rectifiable space containing a dense compactly generated rectifiable subspace is compactly generated; (2) a metriable rectifiable space is compactly generated if and only if it is sigma-compact and finitely generated modulo open sets; (3) any sigma-compact paratopological group can be embedded as a closed paratopological subgroup in some compactly generated paratopological group. Finally, we consider generalized metric properties of compactly generated rectifiable spaces.

引用

页码：417 / 427

页数：11

共 21 条

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