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首页> 外文期刊>Journal of Functional Analysis >Representations of starshaped sets in normed linear spaces
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Representations of starshaped sets in normed linear spaces

机译：赋范线性空间中星形集的表示

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If S is a closed connected nonconvex locally compact and bounded subset of a real normed linear space or a closed connected nonconvex and bounded subset of a real reflexive Banach space, then ker S = boolean AND{cl conv S-z: z is an element of D boolean AND reg S}. where reg S denotes the set of regular points: of S, D is a relatively open subset of S containing the set inc S of local nonconvexity points of S, and S-z = {s is an element of S:z is visible from s via S}. An analogous intersection formula, with the set sph S of spherical points of S in place of reg S is shown to hold for a closed connected nonconvex and hounded subset S of a real Banach space which is uniformly convex and uniformly smooth. if the assumption of boundedness of S is dropped, then in all specified settings the above representations hold with intersections of conv S-z in place of cl conv S-z. This strengthens and complements results of Borwein and Strojwas, Stavrakas, and the author. Finally, the possibility of generating similar intersection formulae in other configuration set-space is discussed. (C) 2000 Academic Press. [References: 20]
机译：如果S是实范数线性空间的闭合连接非凸局部紧致和有界子集或实反身Banach空间的闭合连接非凸局部有界和子集，则ker S =布尔AND {cl conv Sz：z是D的元​​素布尔AND reg S}。其中reg S表示S的正则点集合：D是S的相对开放子集，包含S的局部非凸点的集合inc S，Sz = {s是S的元素： S}。一个相似的交集公式，用S的球点的sph S代替reg S来表示，它适用于均匀凸和均匀光滑的真实Banach空间的闭合连接的非凸和带阴影的子集S。如果舍弃了S的有界性假设，则在所有指定的设置中，上述表示形式都用conv S-z的交集代替cl conv S-z。这加强并补充了Borwein和Strojwas，Stavrakas和作者的结果。最后，讨论了在其他配置集空间中生成相似交集公式的可能性。 （C）2000学术出版社。 [参考：20]

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