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On the Semitopological Extended Bicyclic Semigroup with Adjoined Zero

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It is shown that every Hausdorff locally compact semigroup topology on the extended bicyclic semigroup with adjoined zero \( {C}_{\mathrm{\mathbb{Z}}}^0 \) is discrete. At the same time, on \( {C}_{\mathrm{\mathbb{Z}}}^0 \), there exist 𝔠 different Hausdorff locally compact shift-continuous topologies. In addition, on \( {C}_{\mathrm{\mathbb{Z}}}^0 \), we construct a unique minimal shift-continuous topology and a unique minimal inverse semigroup topology.

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  1. I. Franko Lviv National University, Lviv, Ukraine

    O. V. Gutik & K. M. Maksymyk

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  1. O. V. Gutik
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  2. K. M. Maksymyk
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Published in Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 62, No. 4, pp. 28–38, October–December, 2019.

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Gutik, O.V., Maksymyk, K.M. On the Semitopological Extended Bicyclic Semigroup with Adjoined Zero. J Math Sci 265, 369–381 (2022). https://doi.org/10.1007/s10958-022-06058-6

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