Weierstrass M-test for continuous functions

When the set $X$ in the statement of the Weierstrass M-test is a topological space, a strengthening of the hypothesis produces a stronger result. When the functions $f_n$ are continuous, then the limit of the series $f={\sum }_{n=1}^{\mathrm{\infty }}{f}_n$ 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