Generic Compacta from Relations between Finite Graphs: Theory Building and Examples
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.15228
- arXiv:
- arXiv:2408.15228
- Bibcode:
- 2024arXiv240815228B
- Keywords:
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- Mathematics - General Topology;
- 05C62;
- 54D80;
- 54F15
- E-Print:
- 63 pages