9 research outputs found
Metrizability of Clifford topological semigroups
We prove that a topological Clifford semigroup is metrizable if and only
if is an -space and the set of idempotents of is
a metrizable -set in . The same metrization criterion holds also
for any countably compact Clifford topological semigroup .Comment: 4 page
The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups
In this paper we search for conditions on a countably compact
(pseudo-compact) topological semigroup under which: (i) each maximal subgroup
in is a (closed) topological subgroup in ; (ii) the Clifford part
(i.e. the union of all maximal subgroups) of the semigroup is a
closed subset in ; (iii) the inversion is continuous; and (iv) the projection ,
, onto the subset of idempotents of ,
is continuous
On operations on some classes of discontinuous maps
A map between topological spaces is calledscatteredly continuous (pointwise discontinuous) if for eachnon-empty (closed) subspace the restriction has a point of continuity. We define a map to be weaklydiscontinuous if for every non-empty subspace the set of discontinuity points of the restriction isnowhere dense in .In this paper we consider the composition, Cartesian and diagonalproduct of weakly discontinuous, scatteredly continuous andpointwise discontinuous maps
On operations on some classes of discontinuous maps
A map between topological spaces is called scatteredly continuous (pointwise discontinuous) if for each non-empty (closed) subspace the restriction has a point of continuity. We define a map to be weakly discontinuous if for every non-empty subspace the set of discontinuity points of the restriction is nowhere dense in .In this paper we consider the composition, Cartesian and diagonal product of weakly discontinuous, scatteredly continuous and pointwise discontinuous maps.<br /