Topological embeddings into transformation monoids
S. Bardyla, L. Elliott, J. D. Mitchell, Y. Peresse

TL;DR
This paper characterizes which topological semigroups can be embedded into transformation monoids like $ abla$ and $I_ abla$, providing new examples and conditions related to their topological and algebraic structures.
Contribution
It offers a comprehensive characterization of topological semigroups embeddable into transformation monoids, addressing open problems and establishing new conditions for metrizability and continuity.
Findings
Characterized embeddability of various classes of semigroups into $ abla$ and $I_ abla$
Constructed examples of countable Polish semigroups not embeddable into $ abla$
Provided conditions for metrizability and automatic continuity in Clifford semigroups.
Abstract
In this paper we consider the questions of which topological semigroups embed topologically into the full transformation monoid or the symmetric inverse monoid with their respective canonical Polish semigroup topologies. We characterise those topological semigroups that embed topologically into 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 . We construct several examples of countable Polish topological semigroups that do not embed into , 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…
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Taxonomy
Topicssemigroups and automata theory · Advanced Topology and Set Theory · Computability, Logic, AI Algorithms
