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Every transformation monoid comes equipped with a canonical topology, the topology of pointwise convergence. For some structures, the topology of the endomorphism monoid can be reconstructed from its underlying abstract monoid. This phenomenon is called . In this paper we show that whenever the automorphism group of a countable saturated structure has automatic homeomorphicity and a trivial center, then the monoid of elementary self-embeddings has automatic homeomorphicity, too. As a second result we strengthen a result by Lascar by showing that whenever  is a countable -categorical -finite structure whose automorphism group has a trivial center and if  is any other countable structure, then every isomorphism between the monoids of elementary self-embeddings is a homeomorphism.

Reconstructing the Topology of the Elementary Self-embedding Monoids of Countable Saturated Structures