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arXiv · 2409.03490

On locally compact shift-continuous topologies on semigroups $\mathscr{C}_{+}(a,b)$ and $\mathscr{C}_{-}(a,b)$ with adjoined zero

Oleg Gutik
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Abstract

Let $\mathscr{C}_{+}(p,q)^0$ and $\mathscr{C}_{-}(p,q)^0$ be the semigroups $\mathscr{C}_{+}(a,b)$ and $\mathscr{C}_{-}(a,b)$ with the adjoined zero. We show that the semigroups $\mathscr{C}_{+}(p,q)^0$ and $\mathscr{C}_{-}(p,q)^0$ admit continuum many different Hausdorff locally compact shift-continuous topologies up to topological isomorphism.

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Oleg Gutik. 2024-09-05. On locally compact shift-continuous topologies on semigroups $\mathscr{C}_{+}(a,b)$ and $\mathscr{C}_{-}(a,b)$ with adjoined zero. https://doi.org/10.31861/bmj2024.01.02.

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