On Approximate Continuity of Multivalued Functions
by
Grazyna Kwiecinska
University of Gdansk

An interesting class of real functions of real variable, the approximately continuous functions, was introduced by Denjoy in his work [1] on derivatives.

It was observed in [5] that the real valued functions continuous relative to the approximate topology in the domain and usual topology in the range, turn out to be exactly the approximately continuous functions. A set E is open in this topology and is called d-open, if it is measurable and if the density of E exists and is equel to 1 at every point of E. This topology is called d-topology and is denoted T_d (see [3] or [4]).

In this paper we discus the above property in the case of multivalued function from a measurable space into arbitrary uniform space.

This work was supported by the University of Gda\'nsk, grant BW Nr 5100-5-0151-4

Date received: June 24, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaj-29.