# theorem about continuous convergence

Let $(X,d)$ and $(Y,\rho)$ be metric spaces, and let $f_{n}:X\longrightarrow Y$ be a sequence of continuous functions. Then $f_{n}$ converges continuously to $f$ if and only if $f_{n}$ converges uniformly to $f$ on every compact subset of $X$.

Title theorem about continuous convergence TheoremAboutContinuousConvergence 2013-03-22 14:05:00 2013-03-22 14:05:00 gumau (3545) gumau (3545) 5 gumau (3545) Theorem msc 54A20