Selections and representations of multifunctions in paracompact spaces

Bressan, Alberto; Colombo, Giovanni

Studia Mathematica, Tome 103 (1992), p. 209-216 / Harvested from The Polish Digital Mathematics Library

Résumé

Let (X,T) be a paracompact space, Y a complete metric space, $F : X \to 2^{Y}$ a lower semicontinuous multifunction with nonempty closed values. We prove that if $T^{+}$ is a (stronger than T) topology on X satisfying a compatibility property, then F admits a $T^{+}$ -continuous selection. If Y is separable, then there exists a sequence $(f_{n})$ of $T^{+}$ -continuous selections such that $F (x) = \bar{f_{n} (x); n \geq 1}$ for all x ∈ X. Given a Banach space E, the above result is then used to construct directionally continuous selections on arbitrary subsets of ℝ × E.

Publié le : 1992-01-01

Zbl 0807.54020

EUDML-ID : urn:eudml:doc:215923

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     author = {Alberto Bressan and Giovanni Colombo},
     title = {Selections and representations of multifunctions in paracompact spaces},
     journal = {Studia Mathematica},
     volume = {103},
     year = {1992},
     pages = {209-216},
     zbl = {0807.54020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv102i3p209bwm}
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Bressan, Alberto; Colombo, Giovanni. Selections and representations of multifunctions in paracompact spaces. Studia Mathematica, Tome 103 (1992) pp. 209-216. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv102i3p209bwm/

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