Weierstrass M-test for continuous functions

When the set X in the statement of the Weierstrass M-testMathworldPlanetmathPlanetmath is a topological spaceMathworldPlanetmath, a strengthening of the hypothesis produces a stronger result. When the functions fn are continuousMathworldPlanetmath, then the limit of the series f=n=1fn is also continuous.

The proof follows directly from the fact that the limit of a uniformly convergent sequence of continuous functions is continuous.

Title Weierstrass M-test for continuous functions
Canonical name WeierstrassMtestForContinuousFunctions
Date of creation 2013-03-22 16:08:48
Last modified on 2013-03-22 16:08:48
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 4
Author CWoo (3771)
Entry type Corollary
Classification msc 30A99