%0 Journal Article
%T A study of extremally disconnected topological spaces
%A Alexander Arhangel¡¯skii
%J Bulletin of Mathematical Sciences
%@ 1664-3615
%D 2011
%I Springer
%R 10.1007/s13373-011-0001-8
%X We show that if an extremally disconnected space X has a homogeneous compactification, then X is finite. It follows that if a totally bounded topological group has a dense extremally disconnected subspace, then it is finite. The techniques developed in this article also imply that if the square of a topological group G has a dense extremally disconnected subspace, then G is discrete. See also Theorem 3.12. We also establish a sufficient condition for an extremally disconnected topological ring to be discrete (Theorem 3.9). A theorem on the structure of an arbitrary homeomorphism of an extremally disconnected topological group onto itself is proved (see Theorem 3.7 and Corollary 3.8).
%K Extremally disconnected
%K Compactification
%K Topological group
%K Dyadic compactum
%K Homogeneous space
%K Totally bounded group
%K Primary 54A25
%K Secondary 54B05
%U http://link.springer.com/article/10.1007/s13373-011-0001-8