Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I have two questions to ask regarding uniform convergence for sequences of functions.

So I know that if a sequence ofcontinuousfunctions f_n : [a,b] -> R converge uniformly to functionf, thenfis continuous.

Is this true if "continous" is replaced with "piecewise continuous"? (I am not assuming that the sequence functions are discontinuous at the same points)

i.e. if f_n are each discontinuous at finitely many points, is the uniform limit function f discontinuous at finitely many points as well?

Also, does anyone know for what kinds of metric spaces (if any) is "pointwise convergence" for sequences of functions equivalent to "uniform convergence"?

Thanx.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Uniform convergence

Loading...

Similar Threads - Uniform convergence | Date |
---|---|

Proof uniform convergence -> continuity: Why use hyperhyperreals? | Feb 15, 2014 |

Uniform convergence and derivatives question | Jun 22, 2012 |

Question on uniform convergence | Nov 10, 2011 |

Uniform Convergence of nx/nx+1 | Oct 24, 2011 |

Uniform convergence | Aug 27, 2011 |

**Physics Forums - The Fusion of Science and Community**