DagSemProc.04351.9.pdf
- Filesize: 202 kB
- 7 pages
Document
Compactness in apartness spaces?
Authors
-
Part of:
Volume:
Dagstuhl Seminar Proceedings, Volume 4351
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2005-04-19
Cite AsGet BibTex
Douglas Bridges, Hajime Ishihara, Peter Schuster, and Luminita S. Vita. Compactness in apartness spaces?. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)
https://doi.org/10.4230/DagSemProc.04351.9
https://doi.org/10.4230/DagSemProc.04351.9
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.
Keywords
- Apartness
- constructive
- compact uniform space
Metrics
- Access Statistics
-
Total Accesses (updated on a weekly basis)
0PDF Downloads