International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 513-528

LNC points for m-convex sets

Marilyn Breen

Department of Mathematics, The University of Oklahoma, Norman 73019, Oklahoma, USA

Received 8 April 1980; Revised 4 September 1980

Copyright © 1981 Marilyn Breen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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, QU is expressible as a union of k or fewer (d2)-dimensional manifolds, each containing q For S compact, if to every qQ 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 (d2)-manifolds.

For q any lnc point of S and N a convex neighborhood of q, N bdry  SQ That is, Q is nowhere dense in bdry S. Moreover, if conv(QN)S then QN is not homeomorphic to a (d1)-dimensional manifold.