On automatic homeomorphicity for transformation monoids
| Autor: | Maja Pech, Christian Pech |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Pointwise convergence
Monoid Rational number Pure mathematics Topological monoid General Mathematics 010102 general mathematics Mathematics::General Topology 0102 computer and information sciences Mathematics - Logic Mathematics - Rings and Algebras Urysohn and completely Hausdorff spaces 08A35 (Primary) 54H15 03C15 03C50 (Secondary) 01 natural sciences 010201 computation theory & mathematics Rings and Algebras (math.RA) Homeomorphism (graph theory) Mathematics::Category Theory FOS: Mathematics Countable set 0101 mathematics Partially ordered set Logic (math.LO) Mathematics |
| Popis: | Transformation monoids carry a canonical topology --- the topology of point-wise convergence. A closed transformation monoid $\mathfrak{M}$ is said to have automatic homeomorphicity with respect to a class $\mathcal{K}$ of structures, if every monoid-isomorphism of $\mathfrak{M}$ to the endomorphism monoid of a member of $\mathcal{K}$ is automatically a homeomorphism. In this paper we show automatic homeomorphicity-properties for the monoid of non-decreasing functions on the rationals, the monoid of non-expansive functions on the Urysohn space and the endomorphism-monoid of the countable universal homogeneous poset. 21 pages |
| Databáze: | OpenAIRE |
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