International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 513-528
LNC points for -convex sets
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 be closed, -convex subset of , locally a full -dimensional, with the corresponding set of lnc points of . If is an essential lnc point of order then for some neighborhood of , is expressible as a union of or fewer -dimensional manifolds, each containing For compact, if to every there corresponds a such that is an essential lnc point of order then may be written as a finite union of -manifolds.
For any lnc point of and a convex neighborhood of , That is, is nowhere dense in . Moreover, if then is not homeomorphic to a -dimensional manifold.