SEMITOPOLOGICAL GROUPS AND THE THEOREMS OF MONTGOMERY AND ELLIS

被引：0

作者：

Arhangel'skii, Alexander V. ^{[1
]}

Choban, Mitrofan M.

机构：

[1] Ohio Univ, Dept Math, Athens, OH 45701 USA

来源：

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES | 2009年 / 62卷 / 08期

关键词：

topological group; semitopological group; paratopological group; Baire property; fan-complete; Cech-complete; analytic set; pseudocompact; sieve-complete; TOPOLOGICAL-GROUPS;

D O I：

暂无

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

A class of fan-complete spaces is introduced. Every C(delta)-subspace of a pseudocompact space is fan-complete. Our main result is that a paratopological group is a topological group provided it contains a dense fan-complete subspace. If a semitopological group G contains a dense Coch-complete (sieve-complete) subspace, then C is a Cech-complete topological group. This improves some results of A. Bouziad, P. Kenderov, I. S. Kortezov, and W. B. Moors. Some other new results are obtained (see, in particular, Theorem 10 and Corollary 14).

引用

页码：917 / 922

页数：6

共 13 条

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