60 research outputs found
On locally compact semitopological -bisimple inverse -semigroups
We describe the structure of Hausdorff locally compact semitopological
-bisimple inverse -semigroups with compact maximal subgroups. In
particular, we show that a Hausdorff locally compact semitopological
-bisimple inverse -semigroup with a compact maximal subgroup is
either compact or topologically isomorphic to the topological sum of its
-classes. We describe the structure of Hausdorff locally compact
semitopological -bisimple inverse -semigroups with a monothetic
maximal subgroups. In particular we prove the dichotomy for locally
compact semitopological Reilly semigroup
with adjoined zero and
with a non-annihilating homomorphism : is
either compact or discrete. At the end we discuss on the remainder under the
closure of the discrete Reilly semigroup
in a semitopological semigroup.Comment: 26 page
On countably compact 0-simple topological inverse semigroups
We describe the structure of 0-simple countably compact topological inverse
semigroups and the structure of congruence-free countably compact topological
inverse semigroups
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