License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/DagSemProc.04351.9
URN: urn:nbn:de:0030-drops-1175
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Bridges, Douglas ; Ishihara, Hajime ; Schuster, Peter ; Vita, Luminita S.

Compactness in apartness spaces?

04351.BridgesDouglas1.Paper.117.pdf (0.2 MB)


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

  author =	{Bridges, Douglas and Ishihara, Hajime and Schuster, Peter and Vita, Luminita S.},
  title =	{{Compactness in apartness spaces?}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  pages =	{1--7},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-1175},
  doi =		{10.4230/DagSemProc.04351.9},
  annote =	{Keywords: Apartness , constructive , compact uniform space}

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

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