Approximability of operators in constructive metric spaces

The possibility is studied of approximating pointwise defined operators in a broad class of constructive metric spaces. Various ways of representing operators approximately are presented; uniform approximability, approximability, and weak approximability (see Definitions 3.1, 4.2). It is proved that the class of uniformly approximable operators equals the class of uniformly continuous operators. It is also proved that the class of approximable operators equals the class of weakly approximable operators and coincides with the class of operators having the following property: for every natural number $n$, it is possible to construct a denumerable covering of the domain of the operator by balls such that the operator has oscillation less than $2^{-n}$ in each ball.