On a semitopological extended bicyclic semigroup with adjoined zero

Abstract

In the paper it is shown that every Hausdorff locally compact semigroup topology on the extended bicyclic semigroup with adjoined zero ${\mathcal{C}}_{\mathbb{Z}}^0$ is discrete, but on ${\mathcal{C}}_{\mathbb{Z}}^0$ there exist $\mathfrak{c}$ many different Hausdorff locally compact shift-continuous topologies. Also, it is constructed on ${\mathcal{C}}_{\mathbb{Z}}^0$ the unique minimal shift continuous topology and the unique minimal inverse semigroup topology.

arXiv comment8 pages. arXiv admin note: text overlap with arXiv:1805.04995