On automatic homeomorphicity for transformation monoids

Abstract

Transformation monoids carry a canonical topology --- the topology of point-wise convergence. A closed transformation monoid $\mathfrak{M}$ is said to have automatic homeomorphicity with respect to a class $\mathcal{K}$ of structures, if every monoid-isomorphism of $\mathfrak{M}$ to the endomorphism monoid of a member of $\mathcal{K}$ is automatically a homeomorphism. In this paper we show automatic homeomorphicity-properties for the monoid of non-decreasing functions on the rationals, the monoid of non-expansive functions on the Urysohn space and the endomorphism-monoid of the countable universal homogeneous poset.

21 pages

Cited by in corpus (5)

• Reconstructing the topology on monoids and polymorphism clones of the rationals
• Polish topologies on endomorphism monoids of relational structures
• Automatic continuity, unique Polish topologies, and Zariski topologies on monoids and clones
• Topological embeddings into transformation monoids
• On a stronger reconstruction notion for monoids and clones