A point-free characterisation of Bishop locally compact metric spaces | Zendy

Tatsuji Kawai | Zendy

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A point-free characterisation of Bishop locally compact metric spaces

Author(s) -

Tatsuji Kawai

Publication year - 2017

Publication title -

journal of logic and analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.278

H-Index - 4

ISSN - 1759-9008

DOI - 10.4115/jla.2017.9.c2

Subject(s) - mathematics , locally compact space , metric space , metric (unit) , topology (electrical circuits) , constructive , convex metric space , relatively compact subspace , compact open topology , topological space , space (punctuation) , uniform continuity , compact space , pure mathematics , discrete mathematics , combinatorics , functional analysis , interpolation space , computer science , biochemistry , operations management , chemistry , process (computing) , economics , gene , operating system

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.

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