Suborbits in Knaster's problem

  title={Suborbits in Knaster's problem},
  author={B. Bukh and R. Karasev},
  journal={Bulletin of The London Mathematical Society},
  • B. Bukh, R. Karasev
  • Published 2014
  • Mathematics
  • Bulletin of The London Mathematical Society
  • Abstract. In this paper we exhibit a similarity between Euclidean Ramsey problemsand Knaster-type problems. By borrowing ideas from Ramsey theory we prove weakKnaster properties of non-equatorial triangles in spheres, and of simplices in Euclideanspaces. 1. IntroductionThe Borsuk–Ulam theorem asserts that for every continuous map f: S d → R d thereis a pair of antipodal points x,−x such that f(x) = f(−x). Hopf [11] extended this,he showed that for any two points x,y ∈ S d and any continuous f… CONTINUE READING


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