A topological characterisation of endomorphism monoids of countable structures
arXiv:1508.07404 · doi:10.1007/s00012-017-0427-2
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.
16 pages; minor corrections have been made in version 2