On a theorem of Choquet and Dolecki
type: Item
instance of: scholarly article
title: On a theorem of Choquet and Dolecki
zbMATH Open document ID: 0652.54015
DOI: 10.1016/0022-247X(87)90069-2
author: Iwo Labuda
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: The author clarifies and extends slightly the work of \textit{S. Dolecki}, and \textit{A. Lechicki} [C. R. Acad. Sci., Paris, Ser. I 293, 219-221 (1981; Zbl 0486.54003); J. Math. Anal. Appl. 88, 547-554 (1982; Zbl 0503.54023)] and \textit{R. W. Hansell}, \textit{J. E. Jayne}, the author and \textit{C. A. Rogers} [Math. Z. 189, 297-318 (1985; Zbl 0544.54016)]. Let X, Y be Hausdorff spaces and F:X\(\to Y\) 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 neighborhood U of x such that F(U)\(\setminus F(x)\subset V\). 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.
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 4064024
zbMATH Keywords: upper semicontinuous set-valued map
zbMATH Keywords: smallest possible peak
MaRDI profile type: Publication
cites work: Q5788019
cites work: Q4186101
cites work: Q3946767
cites work: On structure of upper semicontinuity
cites work: Metric characterizations of upper semicontinuity
cites work: On Banach spaces whose dual balls are not weak\(^*\) sequentially compact
cites work: Boundaries of and selectors for upper semi-continuous multi-valued maps
cites work: Upper semi-continuous set-valued functions
cites work: Borel selectors for upper semi-continuous multi-valued functions
cites work: Q3226265
cites work: On a question of H.H. Corson and some related problems
cites work: A Device Of R. J. Whitley's Applied to Pointwise Compactness in Spaces of Continuous Functions
description: scientific article; zbMATH DE number 4064024