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I find it not easy to understand the proof of corollary 0.21 of Hatcher's algebraic toplology. If the question of the title is true, I can understand it. But I don't know how to prove it. Can somebody helps me? Thank you!

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    $\begingroup$ Your edit asks a completely different question. Please ask that in another post. $\endgroup$ Jan 31, 2015 at 9:00
  • $\begingroup$ OK. I will do it. $\endgroup$ Jan 31, 2015 at 9:00

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Consider the inclusion of the circle of radius one with center at the point $(10,0)$ into the space $X=\mathbb R^2-\{(0,0)\}$.

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  • $\begingroup$ It is such an easy counterexample! $\endgroup$ Jan 31, 2015 at 8:37

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