LNC points form-convex sets

[摘要] LetSbe closed,m-convex subset ofRd,Slocally a fulld-dimensional, withQthe corresponding set of lnc points ofS. Ifqis an essential lnc point of orderkthen for some neighborhoodUofq,Q⋂Uis expressible as a union ofkor fewer(d−2)-dimensional manifolds, each containingqForScompact, if to everyq∈Qthere corresponds ak>0such thatqis an essential lnc point of orderkthenQmay be written as a finite union of(d−2)-manifolds.Forqany lnc point ofSandNa convex neighborhood ofq,N⋂bdry S⊈QThat is,Qis nowhere dense inbdry S. Moreover, ifconv(Q⋂N)⫅SthenQ⋂Nis not homeomorphic to a(d−1)-dimensional manifold.

[学科分类] 数学（综合）