Some Krasnosel'skii numbers for finitely starlike sets in the plane |
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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 subset of the plane. In case (int cl S) S = , then S is finitely starlike if and only if every 4 points of S see via S a common point. In case (int cl S) S has at most countably many components, each a singleton set, then S is finitely starlike if and only if every 5 points of S see via S a common point. Each of the numbers 4 and 5 is best possible. Examples show that these results fail without suitable restrictions on (int cl S) S. Moreover, a final example shows that if a general Krasnosel'skii number . exists to characterize finitely starlike sets in the plane, then > 9. |
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Keywords: | Primary 52 A30 52 A35 Secondary 52 A10 |
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