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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Zero-dimensionality of some pseudocompact groups


Author: Dikran Dikranjan
Journal: Proc. Amer. Math. Soc. 120 (1994), 1299-1308
MSC: Primary 54H11; Secondary 22A05, 54D30, 54F45
MathSciNet review: 1185278
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Abstract: We prove that hereditarily disconnected countably compact groups are zero-dimensional. This gives a strongly positive answer to a question of Shakhmatov. We show that hereditary or total disconnectedness yields zero-dimensionality in various classes of pseudocompact groups.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1185278-9
PII: S 0002-9939(1994)1185278-9
Keywords: Connected group, (totally, hereditarily) disconnected group, zero-dimensional group, connected component, quasi-component, (hereditarily) pseudocompact group, countably compact group, (totally) minimal group, torsion group
Article copyright: © Copyright 1994 American Mathematical Society