Abstract
A nonempty setS in a real topological linear spaceL is said to be quasi-starshaped if and only if there is some pointq in clS such that the subset of points ofS visible viaS fromq is everywhwere dense inS and contains intS, and the set of all such pointsq is called the quasi-kernel ofS and denoted by qkerS. It is proved that forS connected with slncS nonempty ∩{conv Âz:z εslncS}\( \subseteq\) qkerS, where slncS denotes the set of strong local nonconvexity points ofS and Âz={s ε clS:z is clearly visible froms via S}. Familiar procedures generate then the Krasnosel'skii-type characterizations for the dimension of the quasi-kernel ofS. This contributes to an open problem.
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Jakub Oswald gewidmet
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Cel, J. Sets which are almost starshaped. J Geom 62, 36–39 (1998). https://doi.org/10.1007/BF01237598
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DOI: https://doi.org/10.1007/BF01237598