Proof about fundamental class for M exists then M is compact.

In this proof, I can’t see why the claim”this image is compact” is true, and I don’t understand why it implies MM is compact.

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Try to prove the negation, i.e for non compact space Hn=0.H_n=0. See proposition 3.29 in Hatcher.
– Anubhav
2 days ago

  

 

@Anubhav, this paragraph is right after Theorem 3.26, so…
– 6666
2 days ago

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1 Answer
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Image of a compact space under a continuous function is compact. You should know this right, I figure you took General topology?

  

 

I know that, buy why is a cycle compact? why is the map continuous? Moreover, what’s the relation with the compactness of MM?
– 6666
2 days ago