Abstract
We extend the work of Ioffe and Lewis [A. Ioffe and A. Lewis, Critical points of simple functions, Optimization, 57 (2008), pp. 3–16] and relate it to the previous work of Morse [M. Morse, Topologically non-degenerate functions in a compact n-manifold, J. Anal. Math. 7 (1959), p. 243]. We show that the concept of regularity for piecewise linear functions can be explained in geometric topological terms and this explanation leads to a unified view of several concepts of regularity for such functions.
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