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The dimension of the convex kernel and points of local nonconvexity


Author: Nick M. Stavrakas
Journal: Proc. Amer. Math. Soc. 34 (1972), 222-224
MSC: Primary 52A20
DOI: https://doi.org/10.1090/S0002-9939-1972-0298549-0
MathSciNet review: 0298549
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Abstract: Let S be a compact connected subset of $ {R^d}$. A necessary and sufficient condition is given to ensure that the dimension of the convex kernel of S is greater than or equal to k, $ 0 \leqq k \leqq d$. This condition involves a visibility constraint on the points of local nonconvexity of S. As consequences, we obtain new characterizations of the convex kernel of S and the nth-order convex kernel of S.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0298549-0
Article copyright: © Copyright 1972 American Mathematical Society

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