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A general compactness theorem

Published online by Cambridge University Press:  24 October 2008

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

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
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