Let X and Y be metric spaces. The goal is to study some intermediate classes of functions between the class of all uniformly continuous mappings (briefly, UC) from X into Y and the class C(X,Y) of all continuous functions f:X->Y. These classes, defined below, have been intensively studied in earlier papers mainly in the case when Y=R, the real line. In this paper we study them for general Y. In particular, we will consider the case when X=Y is the complex plane C.
where the arrow --> stands for the inclusion. Between other things we discuss possible equations in (*) for different spaces X and Y.
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Last modified October 20, 2001.