# 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 |
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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 |