On a characterization of quasicontinuous multifunctions. (English) Zbl 0532.54016

Neubrunn, Tibor; Náther, Ondrej

Čas. Pěst. Mat. 107, 294-300 (1982).

The author considers upper and lower semi-quasicontinuous multifunctions from a topological space \(X\) to a set \(Y\) which is the union of a family \(S\) of its subsets. For single-valued functions, where \(Y\) is a topological space and \(S\) is its topology, upper and lower semi-quasi-continuity become the usual continuity, and upper and lower semi-quasicontinuity become quasi- continuity. The author gives a characterization of upper semi- quasicontinuity in terms of quasi-open sets (sets such that \(A\subset \bar A^ 0)\). He gives examples which show that earlier assertions on the characterization of quasicontinuity that have appeared in the literature are not correct.

Reviewer: R.P.Jerrard

MSC:

54C60	Set-valued maps in general topology
28A15	Abstract differentiation theory, differentiation of set functions

Keywords:

upper and lower semi-quasicontinuous multifunctions; quasi-open sets