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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De Gruyter
2016-08-01
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| Series: | Topological Algebra and its Applications |
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| Online Access: | http://www.degruyter.com/view/j/taa.2016.4.issue-1/taa-2016-0002/taa-2016-0002.xml?format=INT |
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doaj-3035f4ed40cc4bbeb2be810fb57d22812021-10-02T03:27:22ZengDe GruyterTopological Algebra and its Applications2299-32312016-08-014110.1515/taa-2016-0002taa-2016-0002Quotients of Strongly Realcompact GroupsMorales L.0Tkachenko M.1Keiser University Latin American Campus, De la gasolinera UNO dos cuadras al sur, San Marcos, Carazo, NicaraguaUniversidad Autónoma Metropolitana, Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, C.P. 09340, Mexico D.F., MexicoA 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.http://www.degruyter.com/view/j/taa.2016.4.issue-1/taa-2016-0002/taa-2016-0002.xml?format=INTExtension of groups Strongly realcompact Strongly Dieudonné complete P-modification Pgroup Quotient group |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Morales L. Tkachenko M. |
| spellingShingle |
Morales L. Tkachenko M. Quotients of Strongly Realcompact Groups Topological Algebra and its Applications Extension of groups Strongly realcompact Strongly Dieudonné complete P-modification Pgroup Quotient group |
| author_facet |
Morales L. Tkachenko M. |
| author_sort |
Morales L. |
| title |
Quotients of Strongly Realcompact Groups |
| title_short |
Quotients of Strongly Realcompact Groups |
| title_full |
Quotients of Strongly Realcompact Groups |
| title_fullStr |
Quotients of Strongly Realcompact Groups |
| title_full_unstemmed |
Quotients of Strongly Realcompact Groups |
| title_sort |
quotients of strongly realcompact groups |
| publisher |
De Gruyter |
| series |
Topological Algebra and its Applications |
| issn |
2299-3231 |
| publishDate |
2016-08-01 |
| description |
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. |
| topic |
Extension of groups Strongly realcompact Strongly Dieudonné complete P-modification Pgroup Quotient group |
| url |
http://www.degruyter.com/view/j/taa.2016.4.issue-1/taa-2016-0002/taa-2016-0002.xml?format=INT |
| work_keys_str_mv |
AT moralesl quotientsofstronglyrealcompactgroups AT tkachenkom quotientsofstronglyrealcompactgroups |
| _version_ |
1716859821284655104 |