continuous convergence

Let $(X,d)$ and $(Y,\rho)$ be metric spaces, and let $f_{n}:X\longrightarrow Y$ be a sequence of functions. We say that $f_{n}$ converges continuously to $f$ at $x$ if $f_{n}(x_{n})\longrightarrow f(x)$ for every sequence $(x_{n})_{n}\subset X$ such that $x_{n}\longrightarrow x\in X$ . We say that $f_{n}$ converges continuously to $f$ if it does for every $x\in X$ .

Title	continuous convergence
Canonical name	ContinuousConvergence
Date of creation	2013-03-22 14:04:58
Last modified on	2013-03-22 14:04:58
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	7
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 54A20
Synonym	converges continuously