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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Presented by A. Szendrei.
Both authors have received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement no. 257039), and the DFG-funded project ‘Homogene Strukturen, Bedingungserfüllungsprobleme, und topologische Klone’ (Project number 622397). The second author has been supported by funding of the Excellence Initiative by the German Federal and State Governments.
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Bodirsky, M., Schneider, F.M. A topological characterisation of endomorphism monoids of countable structures. Algebra Univers. 77, 251–269 (2017). https://doi.org/10.1007/s00012-017-0427-2
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DOI: https://doi.org/10.1007/s00012-017-0427-2