On a topological simple Warne extension of a semigroup
Iryna Fihel, Oleg Gutik, Kateryna Pavlyk

TL;DR
This paper introduces and studies topological $bZ$-Bruck-Reilly and $bZ$-Bruck extensions of (semi)topological monoids, analyzing their topologizations and characterizations of certain classes of semigroups.
Contribution
It generalizes existing topological extensions of monoids to include $bZ$-Bruck-Reilly and $bZ$-Bruck extensions and provides conditions for their topological properties.
Findings
Conditions for the extension to admit only the direct sum topology.
Criteria for coarsening the direct sum topology.
Topological characterizations of $I$-bisimple (semi)topological semigroups.
Abstract
In the paper we introduce topological -Bruck-Reilly and topological -Bruck extensions of (semi)topological monoids which are generalizations of topological Bruck-Reilly and topological Bruck extensions of (semi)topological monoids and study their topologizations. The sufficient conditions under which the topological -Bruck-Reilly (-Bruck) extension admits only the direct sum topology and conditions under which the direct sum topology can be coarsened are given. Also, topological characterizations of some classes of -bisimple (semi)topological semigroups are given.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
