An extremely simple proof of the K-K-M-S Theorem
An extremely simple proof of the K-K-M-S Theorem is given involving only Brouwer's fixed point theorem and some elementary calculus. A function is explicitly given such that a fixed point of it yields an intersection point of a balanced collection of sets together with balancing weights. Moreover, any intersection point of a balanced collection of sets together with balancing weights corresponds to a fixed point of the function. Furthermore, the proof can be used to show $\pi $-balanced versions of the K-K-M-S Theorem, with $\pi $-balancedness as introduced in Billera (1970). The proof makes clear that the conditions made with respect to $\pi $ by Billera can be even weakened.
Volume (Year): 10 (1997)
Issue (Month): 2 ()
|Note:||Received: January 22, 1996; revised version June 9, 1996|
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