Countable compactness and finite powers of topological groups without convergent sequences

We show under MA countable that for every positive integer n there exists a topological group G without non-trivial convergent sequences such that G n is countably compact but G n+1 is not. This answers the finite case of Comfort's Question 477 in the Open Problems in Topology. We also show und...

Full description

Saved in:
Bibliographic Details
Published in:Topology and its applications Vol. 146; pp. 527 - 538
Main Author: Tomita, A.H.
Format: Journal Article
Language:English
Published: Elsevier B.V 2005
Subjects:
Countably compact
Finite power
Linear independence
Martin's Axiom
Suitable set
Topological group
Finite power
Countably compact
Topological group
Suitable set
Martin's Axiom
Linear independence
.
ISSN:0166-8641, 1879-3207
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We show under MA countable that for every positive integer n there exists a topological group G without non-trivial convergent sequences such that G n is countably compact but G n+1 is not. This answers the finite case of Comfort's Question 477 in the Open Problems in Topology. We also show under MA countable +2 < c = c that there are 2 c non-homeomorphic group topologies as above if n⩾2. We apply the construction on suitable sets, answering the finite case of a question of D. Dikranjan on the productivity of suitability and in a topological game defined by Bouziad.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2003.10.008