We obtain an exact estimate for the minimum multiplicity of a continuous finite-to-one mapping of a projective space into a sphere for all dimensions. For finite-to-one mappings of a projective space into a Euclidean space, we obtain an exact estimate for this multiplicity for n = 2, 3. For n ≥ 4, we prove that this estimate does not exceed 4. Several open questions are formulated.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 7, pp. 937–944, July, 2010.
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Zelinskii, Y.B. On a mapping of a projective space into a sphere. Ukr Math J 62, 1090–1097 (2010). https://doi.org/10.1007/s11253-010-0415-6
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DOI: https://doi.org/10.1007/s11253-010-0415-6