uniform convergence

Let X be any set, and let (Y,d) be a metric space. A sequence f1,f2, of functions mapping X to Y is said to be uniformly convergent to another function f if, for each ε>0, there exists N such that, for all x and all n>N, we have d(fn(x),f(x))<ε. This is denoted by fn𝑢f, or “fnf uniformly” or, less frequently, by fnf.

Title uniform convergence
Canonical name UniformConvergence
Date of creation 2013-03-22 13:13:49
Last modified on 2013-03-22 13:13:49
Owner Koro (127)
Last modified by Koro (127)
Numerical id 14
Author Koro (127)
Entry type Definition
Classification msc 40A30
Related topic CompactOpenTopology
Related topic ConvergesUniformly
Defines uniformly convergent