► 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 sameinitial and terminal points are path-homotopic.

Given : X is a path-connected topological space. To prove : a Let f,g : I→X be two paths from…

Answered: Exercise 7.14. Let X be a…

Elementary Linear Algebra (MindTap Course List)

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ISBN:9781305658004

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Chapter4: Vector Spaces

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Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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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.