I just read Ascoli's theorem: A subspace F of C(X,R^n) has compact closure if and only if F is equicontinuous and pointwise bounded.(adsbygoogle = window.adsbygoogle || []).push({});

Then it says, As a corollary: If the collection {fn} of functions in C(X,R^k) is pointwise bounded and equicontinuous, then the sequence (fn) has a uniformly convergent subsequence.

Can anybody tell me why the corollary follows from the theorem?

**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!

# Ascoli's theorem: A subspace F of C(X,R^n)

Loading...

Similar Threads - Ascoli's theorem subspace | Date |
---|---|

A Stokes' theorem on a torus? | Apr 27, 2017 |

I Proof of Stokes' theorem | Apr 8, 2017 |

I Generalisation of Pythagoras theorem | Jul 12, 2016 |

A Non-Abelian Stokes theorem and variation of the EL action | May 31, 2016 |

Geometric Sets and Tangent Subspaces - McInnerney, Example 3 | Feb 18, 2016 |

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