| Autor: |
Bardyla, Serhii, Elliott, Luke, Mitchell, James D., Péresse, Yann |
| Předmět: |
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| Zdroj: |
Forum Mathematicum; Nov2024, Vol. 36 Issue 6, p1537-1554, 18p |
| Abstrakt: |
In this paper we consider the questions of which topological semigroups embed topologically into the full transformation monoid ℕ ℕ or the symmetric inverse monoid I ℕ with their respective canonical Polish semigroup topologies. We characterise those topological semigroups that embed topologically into ℕ ℕ and belong to any of the following classes: commutative semigroups, compact semigroups, groups, and certain Clifford semigroups. We prove analogous characterisations for topological inverse semigroups and I ℕ . We construct several examples of countable Polish topological semigroups that do not embed into ℕ ℕ , which answer, in the negative, a recent open problem of Elliott et al. Additionally, we obtain two sufficient conditions for a topological Clifford semigroup to be metrizable, and prove that inversion is automatically continuous in every Clifford subsemigroup of ℕ ℕ . The former complements recent works of Banakh et al. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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