Explore BrainMass
Share

Having the same homotopy type equivalence

This content was STOLEN from BrainMass.com - View the original, and get the solution, here!

Prove that "having the same homotopy type" is an equivalence relation on the set of topological spaces.

© BrainMass Inc. brainmass.com September 21, 2018, 9:43 am ad1c9bdddf - https://brainmass.com/math/recurrence-relation/homotopy-type-equivalence-74071

Solution Preview

Lemma: if f,f' are homotopic maps from X to Y and g,g' are homotopic
maps from Y to Z, then g o f is homotopic to g' o ...

Solution Summary

This solution is comprised of a detailed explanation to prove that "having the same homotopy type" is an equivalence relation
on the set of topological spaces.

$2.19