Points of local nonconvexity,clear visibility,and starshaped sets in Rd |
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Authors: | Marilyn Breen |
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Institution: | (1) Department of Mathematics, University of Oklahoma, 73019 Norman, Oklahoma, USA |
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Abstract: | Let S be a compact, connected, locally starshaped set in Rd, S not convex. For every point of local nonconvexity q of S, define Aq to be the subset of S from which q is clearly visible via S. Then ker S = {conv Aq: q lnc S}. Furthermore, if every d+1 points of local nonconvexity of S are clearly visible from a common d-dimensional subset of S, then dim ker S = d. |
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Keywords: | Primary 52 A30 52 A35 Secondary 52 A20 |
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