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arXiv · 1911.05977

On a semitopological extended bicyclic semigroup with adjoined zero

Oleg Gutik·Kateryna Maksymyk
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Abstract

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

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Oleg Gutik, Kateryna Maksymyk. 2019-11-14. On a semitopological extended bicyclic semigroup with adjoined zero. https://arxiv.org/abs/1911.05977

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