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- W4249962227 abstract "This study will investigate the dimension of the kernel of a starshaped set, and the following result will be obtained: Let S be a compact set in some linear topological space L. For $1 leqslant k leqslant n$, the dimension of $ker S$ is at least k if and only if for some $varepsilon > 0$ and some n-dimensional flat ${F^n}$ in L, every $f(n,k)$ points of S see via S a common k-dimensional neighborhood in ${F^n}$ having radius $varepsilon$. The number $f(n,k)$ is defined inductively as follows: [ begin {array}{*{20}{c}} {f(2,1) = 4,} hfill {f(n,k) = f(n - 1,k) + n + 2quad {text {for}};3 leqslant n;{text {and}};1 leqslant k leqslant n - 1,} hfill {f(n,n) = n + 1.} hfill end {array} ]" @default.
- W4249962227 created "2022-05-12" @default.
- W4249962227 creator A5055251002 @default.
- W4249962227 date "1979-02-01" @default.
- W4249962227 modified "2023-09-24" @default.
- W4249962227 title "A Helly-Type Theorem for the Dimension of the Kernel of a Starshaped Set" @default.
- W4249962227 doi "https://doi.org/10.2307/2042297" @default.
- W4249962227 hasPublicationYear "1979" @default.
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