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Some results involving weak compactness in C(X), C(υX) and C(X)′

Published online by Cambridge University Press:  20 January 2009

I. Tweddle
I. Tweddle
Affiliation:
University of Stirling
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The main aim of the present note is to compare C(X) and C(υX), the spaces of real-valued continuous functions on a completely regular space X and its real 1–1 compactification υX, with regard to weak compactness and weak countable compactness. In a sense to be made precise below, it is shown that C(X) and C(υX) have the same absolutely convex weakly countably compact sets. In certain circumstances countable compactness may be replaced by compactness, in which case one obtains a nice representation of the Mackey completion of the dual space of C(X) (Theorems 5, 6, 7).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 3 , March 1975 , pp. 221 - 229
Copyright
Copyright © Edinburgh Mathematical Society 1975

References

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