Polymorphism clones of homogeneous structures: gate coverings and automatic homeomorphicity
| Autor: | Maja Pech, Christian Pech |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pointwise convergence
Class (set theory) Algebra and Number Theory 010102 general mathematics Mathematics::General Topology Quantum Physics 0102 computer and information sciences 01 natural sciences Quantitative Biology::Cell Behavior Combinatorics 010201 computation theory & mathematics Clone (algebra) Homeomorphism (graph theory) Countable set Isomorphism 0101 mathematics Partially ordered set Topology (chemistry) Mathematics |
| Zdroj: | Algebra Universalis. (2):1-24 |
| ISSN: | 0002-5240 |
| Popis: | Every clone of functions comes naturally equipped with a topology, the topology of pointwise convergence. A clone $$\mathfrak {C}$$ is said to have automatic homeomorphicity with respect to a class $$\mathcal {K}$$ of clones, if every clone isomorphism of $$\mathfrak {C}$$ to a member of $$\mathcal {K}$$ is already a homeomorphism (with respect to the topology of pointwise convergence). In this paper we study automatic homeomorphicity properties for polymorphism clones of countable homogeneous relational structures. Besides two generic criteria for the automatic homeomorphicity of the polymorphism clones of homogeneous structures we show that the polymorphism clone of the generic poset with strict ordering has automatic homeomorphicity with respect to the class of polymorphism clones of countable $$\omega $$ -categorical structures. Our results extend and generalize previous results by Bodirsky, Pinsker, and Pongracz. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink