# 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.

=================

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

=================