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A general compactness theorem

Published online by Cambridge University Press:  24 October 2008

P. J. Collins
P. J. Collins
Affiliation:
St Edmund Hall, Oxford
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Extract

It is the purpose of this paper to prove a general compactness theorem and deduce from it, as corollaries, the Tychonoff theorem on the product of compact spaces and Ascoli-type theorems giving sufficient conditions for function spaces with the topology of uniform convergence on compact sets to be compact.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 2 , September 1970 , pp. 351 - 354
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Collins, P. J.Product and quotient topological spaces with respect to a nucleus. Quart. J. Math. Oxford Ser. (to appear).Google Scholar
(2)Kelley, J. L.General topology (van Nostrand, 1955).Google Scholar