Perfectly supportable semigroups are \sigma-discrete in each Hausdorff shift-invariant topology

TL;DR

This paper introduces perfectly supportable semigroups and proves they are -discrete in any Hausdorff shift-invariant topology, expanding understanding of their topological properties.

Contribution

It defines perfectly supportable semigroups and establishes their -discreteness in Hausdorff shift-invariant topologies, including subsemigroups of finitely supported relations.

Findings

Perfectly supportable semigroups are -discrete in each Hausdorff shift-invariant topology.

Includes subsemigroups of finitely supported relations containing finitely supported permutations.

Provides a new class of semigroups with specific topological discreteness properties.

Abstract

In this paper we introduce perfectly supportable semigroups and prove that they are \sigma-discrete in each Hausdorff shift-invariant topology. The class of perfectly supportable semigroups includes each subsemigroup S of the semigroup FRel(X) of finitely supported relations on an infinite set X such that S contains the group FSym(X) of finitely supported permutations of X.