×
Beer, Gerald

Upper semicontinuous functions and the Stone approximation theorem. (English) Zbl 0483.41028

J. Approximation Theory 34, 1-11 (1982).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0483.41028

Cited in 2 Reviews
Cited in 16 Documents

MSC:

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A10 Approximation by polynomials

Keywords:

Hausdorff metric; function lattice; epiconvergence; topological convergence of hypographs
Cite Review PDF
Full Text: DOI

References:

[1] Hausdorff, F., Set Theory (1962), Chelsea: Chelsea New York · Zbl 0060.12401
[2] Heil, E., Über die Auswahlsatze von Blaschke und Arzela-Ascoli, Math. Phys. Semesterber., 14, 169-175 (1967) · Zbl 0166.06601
[3] Mosco, U., Convergence of convex sets and of solutions of variational inequalities, Adv. in Math., 3, 510-585 (1969) · Zbl 0192.49101
[4] Naimpally, S. A., Graph topology for function spaces, Trans. Amer. Math. Soc., 123, 267-272 (1966) · Zbl 0151.29703
[5] Protter, M. H.; Morrey, C. B., A First Course in Real Analysis (1977), Springer-Verlag: Springer-Verlag New York · Zbl 0352.26001
[6] Robert, R., Convergence de fonctionnelles convexes, J. Math. Anal. Appl., 45, 533-555 (1974) · Zbl 0299.46014
[7] Royden, H. L., Real Analysis (1968), Macmillan Co.,: Macmillan Co., New York · Zbl 0197.03501
[8] Salinetti, G.; Wets, R., On the relations between two types of convergence for convex functions, J. Math. Anal. Appl., 60, 211-226 (1977) · Zbl 0359.54005
[9] Stone, M. H., A generalized Weierstrass approximation theorem, (Buck, R. C., Studies in Modern Analysis. Studies in Modern Analysis, M.A.A. Studies in Mathematics, Vol. 1 (1962), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J.) · Zbl 0147.11702
[10] Wijsman, R., Convergence of sequences of convex sets, cones and functions, II, Trans. Amer. Math. Soc., 123, 32-45 (1966) · Zbl 0146.18204
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.