2019
Том 71
№ 11

On a mapping of a projective space into a sphere

Zelinskii Yu. B.

Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 7, pp 1090-1097.

Citation Example: Zelinskii Yu. B. On a mapping of a projective space into a sphere // Ukr. Mat. Zh. - 2010. - 62, № 7. - pp. 937–944.

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