  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.

General Topology;Logic