Recovering the boundary path space of a topological graph using\n pointless topology

2018/04/23 by Gilles G. de Castro, de Castro, Gilles G. · 1 citation
Mathematics · #37B10 #54B05 #54B10 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #General Topology (math.GN) #Operator Algebras (math.OA) #Primary: 46L55 #Secondary: 06D22

paper · pdf · doi:10.48550/arxiv.1804.08466

openalex publication_date 2018/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

First, we generalize the definition of a locally compact topology given by\nPaterson and Welch for a sequence of locally compact spaces to the case where\nthe underlying spaces are T₁ and sober. We then consider a certain\nsemilattice of basic open sets for this topology on the space of all paths on a\ngraph and impose relations motivated by the definitions of graph C*-algebra in\norder to recover the boundary path space of a graph. This is done using\ntechniques of pointless topology. Finally, we generalize the results to the\ncase of topological graphs.\n

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• Fibrewise compactifications and generalised limits in commutative and noncommutative topology

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