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# 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.

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## Mathematics Subject Classification

30A99*no label found*

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