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

Oleg Gutik

doi:10.31861/bmj2024.01.02.

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

Group Theory 2024-10-16 v1 General Topology

Authors: 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.

Keywords

topological semigroups topological groups

Cite

@article{arxiv.2409.03490,
  title  = {On locally compact shift-continuous topologies on semigroups $\mathscr{C}_{+}(a,b)$ and $\mathscr{C}_{-}(a,b)$ with adjoined zero},
  author = {Oleg Gutik},
  journal= {arXiv preprint arXiv:2409.03490},
  year   = {2024}
}

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