Proceedings of the Edinburgh Mathematical Society (Series 2)
- Proceedings of the Edinburgh Mathematical Society (Series 2) / Volume 19 / Issue 03 / March 1975, pp 221-229
- Copyright © Edinburgh Mathematical Society 1975
- DOI: http://dx.doi.org/10.1017/S0013091500015480 (About DOI), Published online: 20 January 2009
Research Article
Some results involving weak compactness in C(X), C(υX) and C(X)′
I. Tweddlea1
a1 University of Stirling
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).
(Received September 04 1973)
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