Classifying the Polish semigroup topologies on the symmetric inverse monoid
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914381563953152 |
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| author | Bardyla, Serhii Elliott, Luna Mitchell, James Péresse, Yann |
| author_facet | Bardyla, Serhii Elliott, Luna Mitchell, James Péresse, Yann |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20134 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classifying the Polish semigroup topologies on the symmetric inverse monoid Bardyla, Serhii Elliott, Luna Mitchell, James Péresse, Yann Rings and Algebras General Topology 20M18, 20M20, 22A15, 54H15, 54E35 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. |
| title | Classifying the Polish semigroup topologies on the symmetric inverse monoid |
| topic | Rings and Algebras General Topology 20M18, 20M20, 22A15, 54H15, 54E35 |
| url | https://arxiv.org/abs/2405.20134 |