International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1981 / Article

Open Access

Volume 4 |Article ID 405215 | https://doi.org/10.1155/S0161171281000379

Marilyn Breen, "LNC points for -convex sets", International Journal of Mathematics and Mathematical Sciences, vol. 4, Article ID 405215, 16 pages, 1981. https://doi.org/10.1155/S0161171281000379

LNC points for m-convex sets

Received08 Apr 1980
Revised04 Sep 1980

Abstract

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.

Copyright © 1981 Hindawi Publishing Corporation. 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.


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