Gábor Lukács
On the quasi-component of minimal pseudocompact abelian groups.
Tue, 07/27/2010 - 15:01 — SomNambulAuthors: Gábor Lukács, D. Dikranjan
Subjects: General Topology
AbstractIn this paper, we describe the relationship between the quasi-component q(G)
of a (perfectly) minimal pseudocompact abelian group G and the component
(\widetilde G)_0 of its completion. Specifically, we characterize the pairs
(C,A) of compact connected abelian groups C and subgroups A such that A=q(G)
and C=(\widetilde G)_0. As a consequence, we show that for every positive
integer n or n=\omega, there exist plenty of abelian pseudocompact perfectly
minimal n-dimensional groups G such that the quasi-component of G is not dense
in the connected component of the completion of G.On zero-dimensionality and the connected component of locally pseudocompact groups.
Wed, 09/09/2009 - 22:08 — SomNambulAuthors: Gábor Lukács
Subjects: General Topology
AbstractA topological group is locally pseudocompact if it contains a non-empty open
set with pseudocompact closure. In this note, we study connectedness and
disconnectedness properties of groups G with the property that every closed
subgroup of G is locally pseudocompact. We show that the completion of the
component G_0 of G contains every connected compact subgroup of the completion
of G.
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