T.Banakh
On topological groups (locally) homeomorphic to LF-spaces.
Mon, 04/05/2010 - 15:01 — SomNambulAuthors: T.Banakh, K.Mine, D.Repovs, K.Sakai, T.Yagasaki
Subjects: Group Theory
AbstractWe study topological structure of the direct limit $glim G_n$ of an
increasing sequence of Polish ANR-groups $(G_n)_n$ in the category of
topological groups and find conditions under which the group $glim G_n$ is
(locally) homeomorphic to one of the following LF-spaces: $\IR^m$,
$\IR^\infty$, $l_2$ or $l_2\times\IR^\infty$.Characterizing meager paratopological groups.
Tue, 08/18/2009 - 11:53 — SomNambulAuthors: T.Banakh, I.Guran, A.Ravsky
Subjects: General Topology
AbstractWe prove that a Hausdorff paratopological group G is meager if and only if
there are a nowhere dense subset A of G and a countable subset C in G such that
CA=G=AC.- 2 comments
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The topology of systems of hyperspaces determined by dimension functions.
Tue, 08/18/2009 - 11:53 — SomNambulAuthors: T.Banakh, N.Mazurenko
Subjects: General Topology
AbstractGiven a non-degenerate Peano continuum $X$, a dimension function
$D:2^X_*\to[0,\infty]$ defined on the family $2^X_*$ of compact subsets of $X$,
and a subset $\Gamma\subset[0,\infty)$, we recognize the topological structure
of the system $(2^X,\D_{\le\gamma}(X))_{\alpha\in\Gamma}$, where $2^X$ is the
hyperspace of non-empty compact subsets of $X$ and $D_{\le\gamma}(X)$ is the
subspace of $2^X$, consisting of non-empty compact subsets $K\subset X$ with
$D(K)\le\gamma$.
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