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Apartness, Topology, and Uniformity: a Constructive View
Author(s) -
Bridges Douglas,
Schuster Peter,
Vîţă Luminiţa
Publication year - 2002
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 - 10.1002/1521-3870(200210)48:1+<16::aid-malq16>3.0.co;2-7
Subject(s) - mathematics , constructive , topology (electrical circuits) , pure mathematics , calculus (dental) , combinatorics , computer science , programming language , process (computing) , medicine , dentistry
The theory of apartness spaces, and their relation to topological spaces (in the point–set case) and uniform spaces (in the set–set case), is sketched. New notions of local decomposability and regularity are investigated, and the latter is used to produce an example of a classically metrisable apartness on R that cannot be induced constructively by a uniform structure.