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 Publish in OALib Journal ISSN: 2333-9721 APC: Only $99  Views Downloads  Relative Articles A counterexample to the reconstruction of$ω$-categorical structures from their endomorphism monoids A universality result for endomorphism monoids of some ultrahomogeneous structures On the endomorphism monoids of some groups with abelian automorphism group Factorisation in Topological Monoids AF inverse monoids and the structure of countable MV-algebras A countable series of bisimple$\mathcal{H}$-trivial finitely presented congruence-free monoids A countable family of finitely presented infinite congruence-free monoids Type II$_1\$ factors with arbitrary countable endomorphism group Topological Ramsey numbers and countable ordinals The Bergman property for endomorphism monoids of some Fra？ssé limits More...
Mathematics  2015

# A topological characterisation of endomorphism monoids of countable structures

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Abstract:

A topological monoid is isomorphic to an endomorphism monoid of a countable structure if and only if it is separable and has a compatible complete ultrametric such that composition from the left is non-expansive. We also give a topological characterisation of those topological monoids that are isomorphic to endomorphism monoids of countable omega-categorical structures. Finally we present analogous characterisations for polymorphism clones of countable structures and for polymorphism clones of countable omega-categorical structures.

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