Abstract
It is shown that for an open connected nonconvex set S in a real topological linear space ker\(S = \cap \) conv \(A_z :z \in \), where slnc S denotes the set of strong local nonconvexity points of S and % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa % aaleaacaWG6baabeaakiabg2da9iaacUhacaWGZbGaeyicI4Saam4u % aiaacQdacaWG6baaaa!3EFE! \[ A_z = \{ s \in S:z \] is clearly visible from s viaS . This formula, combined with familiar procedures, generates the Krasnosel'skii-type characterizations for the dimension of the kernel of S in complete separable real metric linear spaces and, provided slncS is bounded, in finite-dimensional Euclidean spaces. The latter generalizes a planar result and settles an open problem.
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Cel, J. An Optimal Krasnosel'skii-type Theorem for an Open Starshaped Set. Geometriae Dedicata 66, 293–301 (1997). https://doi.org/10.1023/A:1004907931405
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DOI: https://doi.org/10.1023/A:1004907931405