Generic Compacta from Relations between Finite Graphs: Theory Building and Examples

2024/08/27 by Adam Bartoš, Bartoš, Adam, Tristan Bice +3 · 1 citation
Mathematics · #Advanced Topology and Set Theory #Rings, Modules, and Algebras #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2408.15228

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 T₁ 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.

Cited by

• A logic of co-valuations

Related

• Finite combinatorics implicit in the basic definitions of topology
• Graph-Like Compacta: Characterizations and Eulerian Loops
• Minimal Finite Models
• Universal end-compactifications of locally finite graphs
• On the homology of locally finite graphs