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

In Baby Rudin, Thm 3.6 states that If p(n) is a sequence in a compact metric space X, then some subsequence of p(n) converges to a point in X.

Why is it not the case that every subsequence of p(n) converges to a point in X? I would think a compact set would contain every sequence (finite or infinite) that originates within it.

Thanks,

pob

**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!

# Convergent sequence in compact metric space

Loading...

Similar Threads - Convergent sequence compact | Date |
---|---|

A Convergence of a cosine sequence in Banach space | Jun 4, 2016 |

Need some kind of convergence theorem for integrals taken over sequences of sets | Jan 22, 2016 |

Sequence is norm convergent implies it's strongly convergent | Nov 8, 2015 |

Convergence of the sequence from Heron's method. | May 25, 2015 |

Every sequence has a convergent subsequence? | Nov 2, 2014 |

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