pointwise convergence

Let $X$ be any set, and let $Y$ be a topological space. A sequence $f_1,f_2,\mathrm{\dots }$ of functions mapping $X$ to $Y$ is said to be pointwise convergent (or simply convergent) to another function $f$, if the sequence $f_n(x)$ converges to $f(x)$ for each $x$ in $X$. This is usually denoted by $f_n\to f$.

Title	pointwise convergence
Canonical name	PointwiseConvergence
Date of creation	2013-03-22 13:15:28
Last modified on	2013-03-22 13:15:28
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	4
Author	Koro (127)
Entry type	Definition
Classification	msc 40A30
Defines	pointwise