Solution of the problem of combinatorial characterization of the dimension of the kernel of a starshaped set |
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Authors: | Jarosław Cel |
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Affiliation: | (1) Warszawska 24b/56, 26-200 Koskie, Poland |
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Abstract: | It is proved for a nonempty proper subset S of a real topological linear space L that kerS ={convAz: z bdryS} and for a close connected nonconvex subset S of L that kerS ={convAz: z slncS}, where bdryS and slncS denote the sets of boundary points and strong local nonconvexity points of S, respectively, and Az = {s S: z is clearly visible from s via S}.This extends previous results and, combined with standard techniques, yields among others two Krasnosel'skii-type characterizations for the dimension of kerS in Rd in case of a nonempty proper set S with bdryS bounded and a closed connected nonconvex set S with lncS bounded.The assumption of boundedness of S turns out to be irrelevant in these criteria.Herrn Professor Dr. Wilhelm Stoll gewidmetResearch partially supported by the grant PB 2 1140 91 01 |
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