# Sequence of Continuous Function, Uniform Convergence and Pointwise Convergence

Not what you're looking for? Search our solutions OR ask your own Custom question.

Let {fn(x)} n-1 ---> infinity be a sequence of continuous functions [0,1] that converges uniformly.

a) Show that there exists M>0 such that

|fn(x)|<= M (nÐ„I 0<x<1)

b) Does the result in part (a) hold if uniform convergence is replaced by pointwise convergence?

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:43 pm ad1c9bdddfhttps://brainmass.com/math/graphs-and-functions/uniform-convergence-pointwise-convergence-58108

#### Solution Summary

Sequences of Continuous Function, Uniform Convergence and Pointwise Convergence are investigated. The solution is detailed and well presented.

$2.49