Two Notions of Sequential Computability of a Function with Jumps
Mariko Yasugi, Yoshiki Tsujii · Electronic Notes in Theoretical Computer Science · 2002
Given a strictly increasing computable sequence of real numbers (with respect to the Euclidean topology), one can define an effective uniform space of the real line, where the elements in the sequence are regarded as isolated. The relation between two notions of computability of real sequences, one with respect to the Euclidean space and one with respect to the uniform space as above, is discussed. As a consequence, we prove the equivalence of two notions of sequential computability of a function which is effectively uniformly continuous on the intervals between the given points and which may jump at those points.