## On generalized Hausdorff semicontinuity of multifunctions.(English)Zbl 0798.54022

The paper deals with a certain characterization of the generalized Hausdorff semicontinuity of multifunctions. The characterization is analogous to the one given in [G. Beer, Hyperspaces of a metric space: an overview, Publ. del. Dip. di Mat. et Appl., Napoli]. Since there are many types of generalizations of the continuity it seems to be useful to use such a type which includes the other ones. It was done in [C. Bruteanu and I. Tevy, Rev. Roum. Math. Pur. Appl. 18, 121-135 (1973; Zbl 0254.26004)], where the so called $${\mathcal S}$$- continuity is introduced with the help of the concept of a local sieve. The same procedure is followed in this paper. In the second part some consequences of the characterization for a quasicontinuity are given.

### MSC:

 54C60 Set-valued maps in general topology 54C08 Weak and generalized continuity

Zbl 0254.26004
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