Quasicontinuous selections for closed-valued multifunctions

Rok, strany: 2002, 67 - 78

We present a new result in the selection theory. A technique which worked only for the spaces $\Bbb Rⁿ$ (equipped with a linear structure) is adapted and used in the topological context. The main result is: Let $X$ be a regular topological space which is a union of pairwise disjoint regularly semiopen precompact sets. Let $Y$ be a topological space, metrizable by a complete metric. Let $F:X \to Y$ be an l.s.c. multifunction with closed values. Then $F$ has a quasicontinuous selection. Moreover, if $X$ is a locally compact $T₂$ space, then for any finite subset $A$ of $X$ there exists a quasicontinuous selection of $F$ which is continuous at any point of $A$.

ISO 690:

Kupka, I. 2002. Quasicontinuous selections for closed-valued multifunctions. In Mathematica Slovaca, vol. 52, no.1, pp. 67-78. 0139-9918.

APA:

Kupka, I. (2002). Quasicontinuous selections for closed-valued multifunctions. Mathematica Slovaca, 52(1), 67-78. 0139-9918.