theorem about continuous convergence

Let $(X,d)$ and $(Y,\rho )$ be metric spaces, and let $f_n:X⟶Y$ 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
Canonical name	TheoremAboutContinuousConvergence
Date of creation	2013-03-22 14:05:00
Last modified on	2013-03-22 14:05:00
Owner	gumau (3545)
Last modified by	gumau (3545)
Numerical id	5
Author	gumau (3545)
Entry type	Theorem
Classification	msc 54A20