On the number of countably compact group topologies on a free Abelian group

被引：3

作者：

Tomita, AH ^{[1
]}

机构：

[1] Univ Sao Paulo, Dept Math, BR-05315970 Sao Paulo, Brazil

来源：

TOPOLOGY AND ITS APPLICATIONS | 1999年 / 98卷 / 1-3期

关键词：

countably compact; homeomorphism; free Abelian; topological group; Martin's Axiom;

D O I：

10.1016/S0166-8641(98)00104-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show under MA(sigma-centered) the existence of at least (2(omega))(+) non-homeomorphic topological group topologies on the free Abelian group of size 2(omega) which make it countably compact and separable. In particular, under GCH the maximum possible number of such topologies is attained. As a corollary, we show the existence of a semigroup which possesses (2(omega))(+) non-homeomorphic semigroup topologies which make it a counterexample for Wallace's Problem. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：345 / 353

页数：9

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