Pointwise compactness on extreme points
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- by Surjit Singh Khurana PDF
- Proc. Amer. Math. Soc. 83 (1981), 347-348 Request permission
Abstract:
It is proved that if $X$ is a compact convex subset of a locally convex space $E$, then the subset $S$ of $A$, the space of all affine, scalar-valued continuous functions on $X$, which is uniformly bounded on $X$ and relatively countably compact in the pointwise topology on ${\text {ext}}(X)$, is relatively compact in the pointwise topology on $X$.References
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- J. D. Pryce, A device of R. J. Whitley’s applied to pointwise compactness in spaces of continuous functions, Proc. London Math. Soc. (3) 23 (1971), 532–546. MR 296670, DOI 10.1112/plms/s3-23.3.532
- D. H. Fremlin and J. D. Pryce, Semi-extremal sets and measure representations, Proc. London Math. Soc. (3) 29 (1974), 502–520. MR 365089, DOI 10.1112/plms/s3-29.3.502
- Robert R. Phelps, Lectures on Choquet’s theorem, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0193470
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 347-348
- MSC: Primary 46A55; Secondary 52A07
- DOI: https://doi.org/10.1090/S0002-9939-1981-0624928-0
- MathSciNet review: 624928