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Estimation of the number of points of a preimage on the complement. (Russian, English) Zbl 1124.55001
Vestn. Mosk. Univ., Ser. I 2006, No. 1, 17-25 (2006); translation in Mosc. Univ. Math. Bull. 61, No. 1, 18-26 (2006).
Summary: For the relative preimage problem, the question of estimation of the number of preimage points on the complement to the second space of a pair is considered. A minimization theorem and also a theorem on simultaneous minimization on the complement and on the whole space are obtained. As a corollary, we give a result on the preimage problem for a system of pair mappings, with special cases the coincidence problem and the common root problem for a finite number of pair mappings.

55M20 Fixed points and coincidences in algebraic topology
54H25 Fixed-point and coincidence theorems (topological aspects)