A theorem on remainders of topological groups

被引：2

作者：

Arhangel'skii, A. V. ^{[1
,2
]}

van Mill, J. ^{[3
]}

机构：

[1] MGU, Moscow, Russia

[2] MPGU, Moscow, Russia

[3] Univ Amsterdam, Amsterdam, Netherlands

来源：

TOPOLOGY AND ITS APPLICATIONS | 2017年 / 220卷

关键词：

Remainder Compactification; Topological group; First-countable; Perfect space; Metrizable; Spread; Pseudocompact; Free sequence; 1ST-COUNTABLE REMAINDER;

D O I：

10.1016/j.topol.2017.02.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It has been established in [7-9] that a non -locally compact topological group G with a first-countable remainder can fail to be metrizable. On the other hand, it was shown in [6] that if Some remainder of a topological group G is perfect, then this remainder is first-countable. We improve considerably this result below: it is proved that in the main case, when G is not locally compact, the space G is separable and metrizable. Some corollaries of this theorem are given, and an example is presented showing that the theorem is sharp. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：189 / 192

页数：4

共 11 条

[1] First countability, tightness, and other cardinal invariants in remainders of topological groups [J].