3. Let X be a topological space and let f: X→ Sn a continuous map to the n-sphere.Prove the following: If f is not surjective, then f is homotopic to a constant map.

Given That : Let X be a topological space and f:X→Sn a continuous map to the n-sphere . Prove That :…

Answered: 3. Let X be a topological space and let…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.5: Permutations And Inverses

Problem 10E: 10. Let and be mappings from to. Prove that if is invertible, then is onto and is...

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3. Let X be a topological space and let f: X→ Sn a continuous map to the n-sphere. Prove the following: If f is not surjective, then f is homotopic to a constant map.