On a mapping of a projective space into a sphere

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.