Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T07:19:09.346Z Has data issue: false hasContentIssue false
  • English
  • Français

Finiteness at infinity

Published online by Cambridge University Press:  20 January 2009

P. A. Firby
P. A. Firby
Affiliation:
The University, Sheffield, England
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.

If X is a Tychonoff topological space, and if βX is the Stone-Cech compactification of X, then βX\X will denote the complement of X in βX. If A is a subset of X, then cl [A: X] will denote the closure of A in X, and int [A: X] will denote the interior of A in X. In Isbell ((3), p. 119) a property of βX\X is called a property which X has at infinity, and it is the aim of this paper to give necessary and sufficient conditions for X to be finite at infinity. Since βX is T1 we can say that if X is finite at infinity, then βX\X is closed in βX. So we lose nothing by restricting our attention to locally compact, Tychonoff spaces, and for the remainder of the paper X will denote such a space.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 4 , December 1971 , pp. 299 - 304
Copyright
Copyright © Edinburgh Mathematical Society 1971

References

REFERENCES

(1) Doss, R., On uniform spaces with a unique structure, Amer. J. Math. 71 (1949), 19–23.CrossRefGoogle Scholar
(2) Gál, I. S., Uniformisable spaces with a unique structure, Pacific J. Math. 9 (1959), 1053–1060.CrossRefGoogle Scholar
(3) Isbell, J. R., Uniform spaces (Mathematical Surveys, No. 12, American Math. Soc., Providence, R.I., 1964). (4)CrossRefGoogle Scholar
(4) Kelley, J. L., General Topology (Van Nostrand, London, 1955).Google Scholar