Selections and representations of multifunctions in paracompact spaces

• Autorzy: Alberto Bressan , Giovanni Colombo
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

directionally continuous selections

Kategorie tematyczne

• 34A60: Differential inclusions
• 54C65: Selections

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1992
• Tom: 102
• Numer: 3
• Strony: 209-216

Daty

wydano

1992

otrzymano

1991-02-07

Twórcy

autor

Alberto Bressan

• S.I.S.S.A., Via Beirut 4, 34014 Trieste, Italy.

autor

Giovanni Colombo

• S.I.S.S.A., Via Beirut 4, 34014 Trieste, Italy.

Bibliografia

• [1] J. P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin 1984.
• [2] A. Bressan,HAMUpper and lower semicontinuous differential inclusions. A unified approach, in: Controllability and Optimal Control, H. Sussmann (ed.), M. Dekker, New York 1989, 21-32.
• [5] A. Bressan and G. Colombo, Boundary value problems for lower semicontinuous differential inclusions, Funkcial. Ekvac., to appear.
• [6] A. Bressan and A. Cortesi, Directionally continuous selections in Banach spaces, Nonlin. Anal. 13 (1989), 987-992.
• [7] E. Michael, Selected selection theorems, Amer. Math. Monthly 63 (1956), 233-238.
• [8] E. Michael, Continuous selections. I, Ann. of Math. 63 (1956), 361-382.