| 概要 |
Borsuk-Ulam’s theorem is a useful theorem of algebraic topology. It states that for any continuous mapping 𝑓 from the n-sphere S^n to ℝ^n, there exists a point x ∈ S^n such that 𝑓(x) = 𝑓(−x). Recently... Kawasaki (2023) introduced Borsuk- Ulam’s theorem to nonlinear optimization. It applied Borsuk-Ulam’s theorem to an n-tuple of parametric optimization problems with parameter u ∈ S^n, and presented an antipodal theorem for them. Further, it showed that given n convex sets in ℝ^n, it is possible to divide each width in half with a hyperplane. In this paper, we take another approach, which weakens the assumptions, simplifies the proofs, and includes a result beyond the scope of Kawasaki (2023). Further, we add a new insight to the ham-sandwich theorem.続きを見る
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Mendeley出力
