Shape analysis via oriented distance functions (Q1328291)

This paper contains further details of and enhancements on results announced in Lect. Notes Pure Appl. Math. 163, 105-139 (1994; Zbl 0807.49035). Constructions introduced in the work induce topologies on subsets of a fixed domain in \(\mathbb{R}^ n\) using set parametrized functions. The role of the family of oriented distance functions is studied and it seems that they introduce topologies that retain the classical geometric properties associated with sets: convexity, exterior normals, mean curvature, \(C^ k\) boundaries, etc.