LNC points for m‐convex sets
Marilyn Breen · International Journal of Mathematics and Mathematical Sciences · 1980
Let S be closed, m‐convex subset of Rd, S locally a full d‐dimensional, with Q the corresponding set of lnc points of S. If q is an essential lnc point of order k then for some neighborhood U of q, Q ⋂ U is expressible as a union of k or fewer (d − 2)‐dimensional manifolds, each containing q For S compact, if to every q ∈ Q there corresponds a k > 0 such that q is an essential lnc point of order k then Q may be written as a finite union of (d − 2)‐manifolds. For q any lnc point of S and N a convex neighborhood of q, N ⋂ bdry S⊈Q That is, Q is nowhere dense in bdry S. Moreover, if conv(Q ⋂ N)⫅S then Q ⋂ N is not homeomorphic to a (d − 1)‐dimensional manifold.