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
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