Quotients of Strongly Realcompact Groups

Quotients of Strongly Realcompact Groups

A topological group is strongly realcompact if it is topologically isomorphic to a closed subgroup of a product of separable metrizable groups. We show that if H is an invariant Čech-complete subgroup of an ω-narrow topological group G, then G is strongly realcompact if and only if G/H is strongly r...

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Bibliographic Details
Main Authors: Morales L., Tkachenko M.
Format: Article
Language:English
Published: De Gruyter 2016-08-01
Series:Topological Algebra and its Applications
Subjects:
Extension of groups
Strongly realcompact
Strongly Dieudonné complete
P-modification
Pgroup
Quotient group
Online Access:http://www.degruyter.com/view/j/taa.2016.4.issue-1/taa-2016-0002/taa-2016-0002.xml?format=INT
Description
Summary:A topological group is strongly realcompact if it is topologically isomorphic to a closed subgroup of a product of separable metrizable groups. We show that if H is an invariant Čech-complete subgroup of an ω-narrow topological group G, then G is strongly realcompact if and only if G/H is strongly realcompact. Our proof of this result is based on a thorough study of the interaction between the P-modification of topological groups and the operation of taking quotient groups.
ISSN:2299-3231

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