A question about book by John Lee

Question

The author first proved the following important theorem - "Unique Lifting Property of the Circle"

Then, the author proved the following corollary.

My question is: if corollary 8.6's assumption underlined by a red line is wrong. When two lifts $\tilde{f_0},\tilde{f_1}$ have the same initial point, they agree at the point $0$ of $[0,1]$. Then they should be identically equal by Theorem 8.3!

$\tilde{f_1}$ and $\tilde{f_2}$ are not lifts of the same map, so Theorem 8.3 doesn't apply. — Jamie Radcliffe, Jan 19 '21 at 03:07

score 5 · Accepted Answer · answered Jan 19 '21 at 03:06

5

I think there is no issue. Theorem 8.3 describes lifts of the same path, whereas Corollary 8.6 describes lifts of distinct paths.

answered Jan 19 '21 at 03:06

Alekos Robotis

26,184

Yes. I just figured out and was writing an answer when I saw your answer. Theorem 8.3 is for a single function. Thanks! – Hamilton Jan 19 '21 at 03:08
No problem. Happy reading. – Alekos Robotis Jan 19 '21 at 03:08

A question about book by John Lee

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