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arXiv · 2405.20134

Classifying the Polish semigroup topologies on the symmetric inverse monoid

Serhii Bardyla·Luna Elliott·James Mitchell·Yann Péresse
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Abstract

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 large finite anti-chains. Also, we show that the monoid endowed with any second countable T_1 semigroup topology is homeomorphic to the Baire space.

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Serhii Bardyla, Luna Elliott, James Mitchell, Yann Péresse. 2024-05-30. Classifying the Polish semigroup topologies on the symmetric inverse monoid. https://doi.org/10.1017/s0013091525101302

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