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Exercise 7.14. Let X be a path-connected topological space. (a) Let f,g: I→ X be two paths from p to q. Show that f~g if and only if f.g~ Cp. (b) Show that X is simply connected if and only if any two paths in X with the same initial and terminal points are path-homotopic.

Exercise 7.14. Let X be a path-connected topological space. (a) Let f,g: I→ X be two paths from p to q. Show that f~g if and only if f.g~ Cp. (b) Show that X is simply connected if and only if any two paths in X with the same initial and terminal points are path-homotopic.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.2: Inner Product Spaces
Problem 94E
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► Exercise 7.14. Let X be a path-connected topological space. (a) Let f,g: I→ X be two paths from p to q. Show that f~g if and only if f.g~ Cp. (b) Show that X is simply connected if and only if any two paths in X with the same initial and terminal points are path-homotopic.
Transcribed Image Text:► Exercise 7.14. Let X be a path-connected topological space. (a) Let f,g: I→ X be two paths from p to q. Show that f~g if and only if f.g~ Cp. (b) Show that X is simply connected if and only if any two paths in X with the same initial and terminal points are path-homotopic.
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