Pettis property for Polish inverse semigroups

TL;DR

This paper investigates the Pettis property in Polish inverse semigroups, showing that unlike Polish groups, not all possess this property, and explores automatic continuity in examples within the symmetric inverse semigroup.

Contribution

It introduces the Pettis property for Polish inverse semigroups, provides examples, and examines automatic continuity, highlighting differences from the group case.

Findings

Not all Polish inverse semigroups have the Pettis property.

Examples of Polish inverse subsemigroups in I(N) are constructed.

Some examples satisfy automatic continuity.

Abstract

We study a property about Polish inverse semigroups similar to the classical theorem of Pettis about Polish groups. In contrast to what happens with Polish groups, not every Polish inverse semigroup have the Pettis property. We present several examples of Polish inverse subsemigroup of the symmetric inverse semigroup I(N) of all partial bijections between subsets of N. We also study whether our examples satisfy automatic continuity.