Quotients of strongly realcompact groups (Q309181)
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scientific article; zbMATH DE number 6624321
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quotients of strongly realcompact groups |
scientific article; zbMATH DE number 6624321 |
Statements
Quotients of strongly realcompact groups (English)
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7 September 2016
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extension of groups
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strongly realcompact
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strongly Dieudonné complete
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P-modification
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P-group
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quotient group
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The authors study the following concepts for topological groups which are analogous to the concepts of real compactness and Dieudonné completeness in topological spaces: A topological group is called strongly real compact (strongly Dieudonné complete) if it is a closed subgroup of a product of second metrizable groups (of a product of metrizable groups). It is noticed that a strongly real compact group is strongly Dieudonné complete. Each uncountable discrete group is strongly Dieudonné complete but not strongly realcompact.NEWLINENEWLINESufficient conditions under which the factor group of a strongly realcompact (strongly Dieudonné complete) group is strongly realcompact (strongly Dieudonné complete) are given. An example is constructed of a pseudocompact group which demonstrates that the class of strongly real compact groups (strongly Dieudonné complete groups) is not closed under extensions.
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