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We present short proofs of two Tverberg-type theorems for cell complexes by S. Hasui, D. Kishimoto, M. Takeda, and M. Tsutaya. One of them states that for any prime power r, any simplicial sphere X of dimension (d+1) (r-1) -1, and any continuous map f: X Rᵈ there are pairwise disjoint faces ₁, , ᵣ of X such that f (₁) f (ᵣ).
Карасев et al. (Thu,) studied this question.