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Problem 11. Suppose that e~ f but f g (i.e., f is not homotopic to g). Is it possible that ge? Explain your answer. [Hint: Assume g~e. What does this imply?]

Problem 11. Suppose that e~ f but f g (i.e., f is not homotopic to g). Is it possible that ge? Explain your answer. [Hint: Assume g~e. What does this imply?]

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem 11:** Suppose that \( e \sim f \) but \( f \not\sim g \) (i.e., \( f \) is not homotopic to \( g \)). Is it possible that \( g \sim e \)? Explain your answer. [Hint: Assume \( g \sim e \). What does this imply?]
Transcribed Image Text:**Problem 11:** Suppose that \( e \sim f \) but \( f \not\sim g \) (i.e., \( f \) is not homotopic to \( g \)). Is it possible that \( g \sim e \)? Explain your answer. [Hint: Assume \( g \sim e \). What does this imply?]
Expert Solution
Step 1

e is homotopic to g and f is not homotopic to g

homotopic relation is an equivalence relation 

here we have to check whether e is homotopic to g or not

 

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