Classifying the Polish semigroup topologies on the symmetric inverse
monoid
Classifying the Polish semigroup topologies on the symmetric inverse
monoid
We classify all Polish semigroup topologies on the symmetric inverse monoid on the natural numbers. This result answers a question of Elliott et al. There are countably infinitely many such topologies. Under containment, these Polish semigroup topologies form a join-semilattice with infinite descending chains, no infinite ascending chains, and arbitrarily …