ON LOCALLY COMPACT SHIFT-CONTINUOUS TOPOLOGIES ON SEMIGROUPS C+(A;B) AND C−(A, B) WITH ADJOINED ZERO
Олег Гутік · Bukovinian Mathematical Journal · 2024
Let $\mathscr{C}_{+}(a,b)$ and $\mathscr{C}_{-}(a,b)$ be upper and down subsemigroups of the bicyclic semigroup defined in \cite{Makanjuola-Umar=1997}. 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.