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Formal continuity implies uniform continuity near compact images on metric spaces
Author(s) -
Palmgren Erik
Publication year - 2014
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201200006
Subject(s) - uniform continuity , mathematics , metric space , constructive , metric (unit) , pure mathematics , uniform limit theorem , compact space , convex metric space , space (punctuation) , locally compact space , mathematical analysis , discrete mathematics , computer science , operations management , process (computing) , economics , operating system
The localic completion of a metric space induces a canonical notion of continuous map between metric spaces. It is shown that these maps are continuous in the sense of Bishop constructive mathematics, i.e., uniformly continuous near every compact image.