Hostname: page-component-848d4c4894-mwx4w Total loading time: 0 Render date: 2024-06-29T17:21:37.097Z Has data issue: false hasContentIssue false
  • English
  • Français

Locally bounded spaces

Published online by Cambridge University Press:  20 January 2009

P. Th. Lambrinos
P. Th. Lambrinos
Affiliation:
University of ThessalonikiGreece
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The three common definitions of local compactness require, respectively, each point to have a compact neighbourhood, a neighbourhood basis consisting of compact sets, or a closed compact neighbourhood. These definitions are equivalent in Hausdorff or in regular spaces but not in general (3, 7).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 4 , September 1975 , pp. 321 - 325
Copyright
Copyright © Edinburgh Mathematical Society 1975

References

REFERENCES

(1) Berri, M. P., Minimal topological spaces, Trans. Amer. Math. Soc. 108 (1963), 97–105.CrossRefGoogle Scholar
(2) Gagola, S. and Gemignani, M., Absolutely bounded sets, Math. Japan 13 (1968), 129–132.Google Scholar
(3) Gross, J. I., A Third definition of local compactness, Amer. Math. Monthly 74 (1967), 1120–1122.CrossRefGoogle Scholar
(4) Kelley, J. L., General Topology (van Nostrand, New York, London, Toronto, 1965).Google Scholar
(5) Lambrinos, P. TH., A topological notion of boundedness, Manuscripta Math. 10 (1973), 289–296.CrossRefGoogle Scholar
(6) Oeconomidis, N., Sur les ensembles bornés dans un espace topologique, An. Fac. Phys. Math. Univ. Thessaloniki (to appear).Google Scholar
(7) Schnare, P. S., Two definitions of local compactness. Amer. Math. Monthly, 72 (1965), 764–765.CrossRefGoogle Scholar
(8) Steen, L. A. and Seebach, J. A. Jr, Counterexamples in Topology (Holt, Rinehart, Winston, New York, 1970).Google Scholar
(9) Ward, A. J., Problem in “Proceedings of the international symposium on topology and its applications, Herceg-Novi, 1968”, p. 352. (Savez Matematičara, Beograd, Yugoslavia, 1969).Google Scholar