Approximation of maps into spheres by piecewise-regular maps of class C^k

Abstract

The aim of this paper is to prove that every continuous map from a compact subset of a real algebraic variety into a sphere can be approximated by piecewise-regular maps of class C^k, where k is an arbitrary integer.

14 pages; minor modifications. arXiv admin note: text overlap with arXiv:1705.04525 by other authors