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arXiv · 1508.07404

A topological characterisation of endomorphism monoids of countable structures

Manuel Bodirsky·Friedrich Martin Schneider
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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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Manuel Bodirsky, Friedrich Martin Schneider. 2015-08-29. A topological characterisation of endomorphism monoids of countable structures. https://doi.org/10.1007/s00012-017-0427-2

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