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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© Copyright 1972
American Mathematical Society
