theorem about continuous convergence

Let (X,d) and (Y,ρ) be metric spaces, and let fn:XY be a sequence of continuous functions. Then fn converges continuously to f if and only if fn 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