Answer the following three questions using Latex.

For Y a metric space and X a topological space, define “ topology of compact convergence “ on C(X,Y)

(Munkres p281 – 282 ) (attached).

If x “compactly generated “

Prove that if{f_n } ¦(8@n=1 ) is a convergent sequence.

Of continuous functions in the topology of compact convergence, then lim-(n?8)?f_(n ) ?C (X,Y)

(Prove of corollary 4.5 on P 283 (attached)– you will need to state and prove Theorem 4.4).

Specialise to care X=Y=O ? C

Need to show convergence when f_n conformal.

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