Fx Analysis Real Analysis, Covering Subsets.?

Real Analysis, covering subsets.? - fx analysis

Prove: If f: M -> N is continuous and A is a subset of the cover of M, then f (A) is supporting compact.

Proof: We know that A is a subset of M, so that for any x in M, X in A. Since F is continuous, because epsilon is greater than 0 fx subepsilon N to N open, so that its preimage is open in M.

The archetype is equal to A. In an open-ended coverage of Part A coverage is also plausible to say that everyone has open subcover A guide as a "finished". A pact includes Do This means that f (A) to support compact.
The last test.

I'm not even near the correct answer, or do I make a circular argument?

Thank you!