Generic Compacta from Relations between Finite Graphs: Theory Building and Examples
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866918138447134720 |
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| author | Bartoš, Adam Bice, Tristan Vignati, Alessandro |
| author_facet | Bartoš, Adam Bice, Tristan Vignati, Alessandro |
| contents | In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset with its spectrum, which is a compact T_1 topological space.
In this paper, we focus on the case where such finite sets have a graph structure and the relations belong to a given graph category. We relate topological properties of the spectrum to combinatorial properties of the graph categories involved. We then utilise this to exhibit elementary combinatorial constructions of well-known continua as Fraïssé limits of finite graphs in categories with relational morphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15228 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generic Compacta from Relations between Finite Graphs: Theory Building and Examples Bartoš, Adam Bice, Tristan Vignati, Alessandro General Topology 05C62, 54D80, 54F15 In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset with its spectrum, which is a compact T_1 topological space. In this paper, we focus on the case where such finite sets have a graph structure and the relations belong to a given graph category. We relate topological properties of the spectrum to combinatorial properties of the graph categories involved. We then utilise this to exhibit elementary combinatorial constructions of well-known continua as Fraïssé limits of finite graphs in categories with relational morphisms. |
| title | Generic Compacta from Relations between Finite Graphs: Theory Building and Examples |
| topic | General Topology 05C62, 54D80, 54F15 |
| url | https://arxiv.org/abs/2408.15228 |