On some kinds of ω-balancedness and (*) properties in certain semitopological groups

IF 0.6 4区 数学 Q3 MATHEMATICS
Liang-Xue Peng
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引用次数: 0

Abstract

In this article, we discuss some relationships of ω-balancedness and () properties which were introduced for giving characterizations of subgroups of topological products of certain para(semi)topological groups. We mainly get the following results.

If G is a regular ω-balanced locally ω-good semitopological group with a q-point, then Ir(G)ω if and only if Sm(G)ω. If G is a regular strongly paracompact semitopological group with a q-point and Sm(G)ω, then G is completely ω-balanced if and only if G has property (). If G is a regular paracompact ω-balanced locally good semitopological group with a q-point and Sm(G)ω, then G has property (w) if and only if G has property (**). If G is a regular metacompact semitopological group with a q-point and Sm(G)ω, then G is MM-ω-balanced if and only if G is M-ω-balanced.

We show that a semitopological group G admits a homeomorphic embedding as a subgroup of a product of metrizable semitopological groups if and only if G is topologically isomorphic to a subgroup of a product of semitopological groups which are first-countable paracompact regular σ-spaces and is topologically isomorphic to a subgroup of a product of Moore semitopological groups.

论某些半坡群中的ω平衡性和(*)性质
本文讨论了ω平衡性和(⁎)性质的一些关系,这些关系是为了给出某些副(半)拓扑群的拓扑积的子群的特征而引入的。如果 G 是一个有 q 点的正则 ω 平衡局部 ω 好半拓扑群,那么当且仅当 Sm(G)≤ω 时,Ir(G)≤ω。如果 G 是一个有 q 点的正则强准紧密半坡群,且 Sm(G)≤ω,那么当且仅当 G 具有(⁎)性质时,G 才是完全ω平衡的。若 G 是一个有 q 点的正则准圆锥ω平衡局部良好半坡群,且 Sm(G)≤ω,则当且仅当 G 具有性质 (**) 时,G 才具有性质 (w⁎)。如果 G 是具有 q 点的正则元紧密半坡群,且 Sm(G)≤ω ,那么只有当 G 是 M-ω 平衡时,G 才是 MM-ω 平衡的。我们证明,当且仅当 G 在拓扑上同构于第一可数paracompact正则σ空间的半坡群积的一个子群,并且在拓扑上同构于摩尔半坡群积的一个子群时,半坡群 G 可以同构嵌入为可元半坡群积的一个子群。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.20
自引率
33.30%
发文量
251
审稿时长
6 months
期刊介绍: Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.
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