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RECOVERING THE BOUNDARY PATH SPACE OF A TOPOLOGICAL GRAPH USING POINTLESS TOPOLOGY

Published online by Cambridge University Press:  04 March 2020

GILLES G. DE CASTRO*
Affiliation:
Departamento de Matemática, Centro de Ciências Físicas e Matemáticas, Universidade Federal de Santa Catarina, 88040-970 Florianópolis SC, Brazil e-mail: gilles.castro@ufsc.br

Abstract

First, we generalize the definition of a locally compact topology given by Paterson and Welch for a sequence of locally compact spaces to the case where the underlying spaces are $T_{1}$ and sober. We then consider a certain semilattice of basic open sets for this topology on the space of all paths on a graph and impose relations motivated by the definitions of graph C*-algebra in order to recover the boundary path space of a graph. This is done using techniques of pointless topology. Finally, we generalize the results to the case of topological graphs.

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by A. Sims

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