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Alexander's theorem for real-compactness

Published online by Cambridge University Press:  24 October 2008

Allan Hayes
Allan Hayes
Affiliation:
University of Leicester
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Extract

Alexander's theorem (5) states that a topological space is compact if there is a sub-base, , for its closed sets such that every subclass of with the finite intersection property has a non-empty intersection. An analysis and extension of this is given here which has applications, inter alia, to problems concerning real-compactness (2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 1 , January 1968 , pp. 41 - 43
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Frolík, Z.On almost real-compact spaces. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 9 (1961), 247–250.Google Scholar
(2)Gillman, L. and Jerison, M.Rings of continuous functions (New York, 1960).CrossRefGoogle Scholar
(3)Halmos, , Paul, R.Measure theory (New York, 1950).CrossRefGoogle Scholar
(4)Hewitt, E.Linear functions on spaces of continuous functions. Fund. Math. 37 (1950), 161–189.CrossRefGoogle Scholar
(5)Kelley, J. L.General topology (New York, 1955).Google Scholar
(6)Negripontis, Stelios. Notices Amer. Math. Soc. 77, 683.Google Scholar