Information on the thesis

In PhD Thesis we construct an example of H-closed topological semilattice
which is not absolutely H-closed. This example gives a negative
answer to the question of James Stepp.
We prove that each non-zero element of a semitopological λ-polycyclic
monoid P_λ is an isolated point and each Hausdorff locally
compact topological λ-polycyclic monoid is discrete. We describe all
Hausdorff locally compact topologies which make P_λ a locally compact
semitopological semigroup. In particular, we show that a Hausdorff lo-
cally compact semitopological polycyclic monoid is either compact or
discrete. In PhD Thesis we show that there exists no feebly compact
topological semigroup which contains monoid P_λ as a dense subsemi-
group. We construct the coarsest Hausdorff inverse semigroup topology
on the λ-polycyclic monoid and find a sufficient conditions for monoid P_λ
to be absolutely H-closed in the class of topological inverse semigroups.
Also in PhD Thesis we investigate the α-bicyclic semigroup Bα and
prove that for each ordinal α <= ω a locally compact Hausdorff topological
monoid B_α is discrete, and an example of non-discrete Hausdorff
locally compact inverse semigroup topology on the semigroup B_ω+1 is
constructed.
Key words: H-closed topological semilattice, semitopological semi-
group, α-bicyclic monoid, polycyclic monoid, locally compact space.