Generalizations of Tucker–Fan–Shashkin Lemmas
Tucker and Ky Fan’s lemma are combinatorial analogs of the Borsuk–Ulam theorem (BUT). In 1996, Yu. A. Shashkin proved a version of Fan’s lemma, which is a combinatorial analog of the odd mapping theorem (OMT). We consider generalizations of these lemmas for BUT–manifolds, i.e. for manifolds that satisfy BUT. Proofs rely on a generalization of the OMT and on a lemma about the doubling of manifolds with boundaries that are BUT–manifolds.
Musin, O.R. Generalizations of Tucker–Fan–Shashkin Lemmas. Arnold Math J. 2, 299–308 (2016). https://doi.org/10.1007/s40598-016-0045-7
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