Original Paper

Apartness, Topology, and Uniformity: a Constructive View

  1. Douglas Bridges1,
  2. Peter Schuster2,
  3. Luminiţa Vîţă1,†

Article first published online: 14 OCT 2002

DOI: 10.1002/1521-3870(200210)48:1+<16::AID-MALQ16>3.0.CO;2-7

Issue

Mathematical Logic Quarterly

Mathematical Logic Quarterly

Supplement: Mathematical Logic Quarterly/Supplement 1

Volume 48, Issue Supplement 1, pages 16–28, October 2002

Additional Information

How to Cite

Bridges, D., Schuster, P. and Vîţă, L. (2002), Apartness, Topology, and Uniformity: a Constructive View. Mathematical Logic Quarterly, 48: 16–28. doi: 10.1002/1521-3870(200210)48:1+<16::AID-MALQ16>3.0.CO;2-7

Author Information

  1. 1

    Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

  2. 2

    Mathematisches Institut, Ludwig–Maximilians–Universität München, Theresienstraße 39, 80333 München, Germany

  1. †

    Catedra de Matematică, Universitatea Dunărea de Jos, Str. Domnească nr. 47, Galaţi, Romania

Publication History

  1. Issue published online: 14 OCT 2002
  2. Article first published online: 14 OCT 2002
  3. Manuscript Revised: 23 APR 2002
  4. Manuscript Received: 14 DEC 2001

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Keywords:

  • Apartness spaces;
  • constructive

Abstract

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.

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