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- W2053352985 abstract "The results of this paper clarify and extend slightly the previous work of Dolecki and Lechicki (C. R. Acad. Sci. Paris, 293 1981, 219–221; J. Math. Anal. Appl., 88 1982, 547–584) and Hansell, Jayne, Rogers and the author (Math. Z., 189 1985, 297–318). Let X, Y be Hausdorff spaces and F: X → Y an upper semicontinuous set-valued map. A subset K of F(x) is said to be a peak of F at x, if, for every open set V containing K, there exists a neighbourhood U of x such that F(U)/F(x)/t(V). Criteria (“Choquet-Dolecki Theorems”) are given in order that F has the smallest possible peak. It turns out that in unexpectedly general situations an upper semicontinuous map F has, for every x in X, a peak which is the smallest possible at x and moreover compact." @default.
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- W2053352985 date "1987-08-01" @default.
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- W2053352985 title "On a theorem of Choquet and Dolecki" @default.
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- W2053352985 doi "https://doi.org/10.1016/0022-247x(87)90069-2" @default.
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