### A point-free characterisation of Bishop locally compact metric spaces

#### Abstract

We give a characterisation of Bishop locally compact metric spaces in terms of formal topology. We identify inhabited enumerably locally compact regular formal topologies as point-free counterpart of Bishop locally compact metric spaces. Specifically, we show that a formal topology is isomorphic to an inhabited enumerably locally compact regular formal topology if and only if it is isomorphic to the localic completion of a Bishop locally compact metric space. The result is obtained in Bishop constructive mathematics with the Dependent Choice.

#### Full Text:

C2. [PDF]DOI: https://doi.org/10.4115/jla.2017.9.c2

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Journal of Logic and Analysis ISSN: 1759-9008