1,201 research outputs found
Homogeneous Subspaces of Products of Extremally Disconnected Spaces
Homogeneous countably compact spaces and whose product is
not pseudocompact are constructed. It is proved that all compact subsets of
homogeneous subspaces of the third power of an extremally disconnected space
are finite. Moreover, under CH, all compact subsets of homogeneous subspaces of
any finite power of an extremally disconnected space are finite and all compact
subsets of homogeneous subspaces of the countable power of an extremally
disconnected space are metrizable. It is also proved that all compact
homogeneous subspaces of finite powers of an extremally disconnected space are
finite, which strengthens Frol\'{\i}k's theorem
Almost paratopological groups
A class of almost paratopological groups is introduced, which (1) contains
paratopological groups and Hausdorff quasitopological groups; (2) is closed
under products; (3) subgroups. Almost paratopological groups are
characterized by the fact that is closed in . A
compact almost paratopological group is topological. A regular -space
with a countable extend and a separately continuous Mal'tsev operation is
-cellular (and ccc). A -compact regular almost paratopological
group is ccc. In particular, a -compact regular quasitopological group
is ccc
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