continuous convergence

Let $(X,d)$ and $(Y,\rho )$ be metric spaces, and let $f_n:X⟶Y$ be a sequence of functions. We say that $f_n$ converges continuously to $f$ at $x$ if $f_n(x_n)⟶f(x)$ for every sequence ${(x_n)}_n\subset X$ such that $x_n⟶x\in X$. 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