Computability on Regular Subsets of Euclidean Space

For the computability of subsets of real numbers, several reasonable notions have been suggested in the literature. We compare these notions in a systematic way by relating them to pairs of ‘basic’ ones. They turn out to coincide for full-dimensional convex sets; but on the more general class of regular sets, they reveal rather interesting ’weaker/stronger’ relations. This is in contrast to single real numbers and vectors where all ‘reasonable’ notions coincide. Mathematics Subject Classification: 03F60,51M04,54H05,65D18.