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