Computable operators on regular sets
Martin Ziegler · Mathematical logic quarterly · 2004
Abstract For regular sets in Euclidean space, previous work has identified twelve ‘basic’ computability notions to (pairs of) which many previous notions considered in literature were shown to be equivalent. With respect to those basic notions we now investigate on the computability of natural operations on regular sets: union, intersection, complement, convex hull, image, and pre‐image under suitable classes of functions. It turns out that only few of these notions are suitable in the sense of rendering all those operations uniformly computable. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)