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A selection theorem for topological convex structures


Author: M. van de Vel
Journal: Trans. Amer. Math. Soc. 336 (1993), 463-496
MSC: Primary 46A99; Secondary 47H04, 54C65
DOI: https://doi.org/10.1090/S0002-9947-1993-1169083-9
MathSciNet review: 1169083
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Abstract: A continuous selection theorem has been obtained for multivalued functions, the values of which are convex sets of certain synthetic convex structures. Applications are given related with superextensions, (semi)lattices, spaces of order arcs, trees, Whitney levels in hyperspaces, and geometric topology. Applications to traditional convexity in vector spaces involve Beer's approximation theorem and a fixed point theorem of Dugundji-Granas. Some other applications (a.o. an invariant arc theorem) appear elsewhere.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1169083-9
Keywords: Absolute retract, compact (semi)lattice, continuous selection, convex hyperspace, convex system, Kakutani separation property, LSC multifunction, metric convex structure, space of order arcs, tree, uniform convex structure, Whitney map
Article copyright: © Copyright 1993 American Mathematical Society

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