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URN: urn:nbn:de:0030-drops-1175
URL: http://drops.dagstuhl.de/opus/volltexte/2005/117/
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Bridges, Douglas ; Ishihara, Hajime ; Schuster, Peter ; Vita, Luminita S.

Compactness in apartness spaces?

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Abstract

A major problem in the constructive theory of apartness spaces is that of finding a good notion of compactness. Such a notion should (i) reduce to ``complete plus totally bounded'' for uniform spaces and (ii) classically be equivalent to the usual Heine-Borel-Lebesgue property for the apartness topology. The constructive counterpart of the smallest uniform structure compatible with a given apartness, while not constructively a uniform structure, offers a possible solution to the compactness-definition problem. That counterpart turns out to be interesting in its own right, and reveals some additional properties of an apartness that may have uses elsewhere in the theory.

BibTeX - Entry

@InProceedings{bridges_et_al:DSP:2005:117,
  author =	{Douglas Bridges and Hajime Ishihara and Peter Schuster and Luminita S. Vita},
  title =	{Compactness in apartness spaces?},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  year =	{2005},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  number =	{04351},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2005/117},
  annote =	{Keywords: Apartness , constructive , compact uniform space}
}

Keywords: Apartness , constructive , compact uniform space
Seminar: 04351 - Spatial Representation: Discrete vs. Continuous Computational Models
Issue Date: 2005
Date of publication: 19.04.2005

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