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 $f=\sum_{n=1}^{\infty}f_{n}$ 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 WeierstrassMtestForContinuousFunctions 2013-03-22 16:08:48 2013-03-22 16:08:48 CWoo (3771) CWoo (3771) 4 CWoo (3771) Corollary msc 30A99