On topological groups containing a Fréchet-Urysohn fan |
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| Author |
Department of Mathematics, Lviv University, Universytetska 1,Lviv, 290602, Ukraine
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| Abstract |
Suppose $G$ is a topological group containing a (closed) topological
copy of the Fréchet-Urysohn fan. If $G$ is a perfectly normal sequential
space (a normal $k$-space) then every closed metrizable subset in $G$ is
locally compact. Applying this result to topological groups whose underlying
topological space can be written as the direct limit of a sequence of closed
metrizable subsets, we get that every such a group either is metrizable or
is homeomorphic to the
product of a $k_\omega$-space and a discrete space.
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| Keywords |
topological group, Fréchet-Urysohn fan, perfectly normal sequential space, normal k-space, closed metrizable subset, locally compact, direct limit
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| DOI |
doi:10.30970/ms.9.2.149-154
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Reference |
1. E. Pentsak On manifolds modeled on direct limits of $C$-universal ANR's// Matematychni Studii V.5 -- 1995 p. 107--116
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| Pages |
149-154
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| Volume |
9
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| Issue |
2
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| Year |
1998
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| Journal |
Matematychni Studii
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