LNC points for m -convex sets

Marilyn Breen

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-16

Abstract:

Let S be closed, m -convex subset of R d , 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.

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:405215

DOI: 10.1155/S0161171281000379

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