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Selections and representations of multifunctions in paracompact spaces

100%

Bressan A., Colombo G.

Studia Mathematica

1992

tom 102

nr 3

209-216

Let (X,T) be a paracompact space, Y a complete metric space, $F:X → 2^Y$ 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 $F(x)=\overline{{f_n(x);n ≥ 1}}$ 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.

Extensions and selections of maps with decomposable values

70%

Bressan A., Colombo G.

Studia Mathematica

1988

tom 90

nr 1

69-86

Ograniczanie wyników

2 Studia Mathematica

2 Bressan A.

2 Colombo G.

1 1992

1 1988

Wyniki wyszukiwania

Selections and representations of multifunctions in paracompact spaces

Extensions and selections of maps with decomposable values