On the dichotomy of a locally compact semitopological polycyclic monoid

Serhii Bardyla

Published 2016-09-09Version 1

In this paper for each non-zero cardinal $\lambda$ we describe all locally compact topologies $\tau$ on the $\lambda$-polycyclic monoid $\mathcal{P}_{\lambda}$ such that $(\mathcal{P}_{\lambda},\tau)$ is a semitopological semigroup. In particular we prove that a locally compact semitopological $\lambda$-Polycyclic monoid is either compact or discrete.