S^2 is the sphere, RP^2 is the real projective plane (a) Every continuous map S² → RP2 is homotopic to the constant map.

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Answered: (a) Every continuous map S2 → RP² is…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter7: Real And Complex Numbers

Section7.2: Complex Numbers And Quaternions

Problem 50E

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(a) Every continuous map S2 → RP² is homotopic to the constant map.