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

✍ Scribed by Artur Hideyuki Tomita

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 88 KB
Volume: 98
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(98)00104-7

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✦ Synopsis

We show under MA(σ -centered) the existence of at least (2 ω ) + non-homeomorphic topological group topologies on the free Abelian group of size 2 ω 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 ω ) + non-homeomorphic semigroup topologies which make it a counterexample for Wallace's Problem.

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