subsimplices

subsimplices

1. plural of subsimplex
   • 2016, A. Skopenkov, “A user's guide to disproof of topological Tverberg conjecture”, in arXiv‎:

     The conjecture asserts that for each integers ${\displaystyle r,d>0}$ and each continuous map ${\displaystyle f\colon \Delta \to \mathbb {R} ^{d}}$ of the ${\displaystyle (d+1)(r-1)}$-dimensional simplex ${\displaystyle \Delta }$ there are pairwise disjoint subsimplices ${\displaystyle \sigma _{1},\ldots ,\sigma _{r}\subset \Delta }$ such that ${\displaystyle f(\sigma _{1})\cap \ldots \cap f(\sigma _{r})\neq \emptyset }$. A counterexample was found in a series of papers by M. \"Ozaydin, M.