a closed set contains all its cluster (accumulation) points: points for which any open neighborhood around them no matter how small contains points from the set.(adsbygoogle = window.adsbygoogle || []).push({});

a complete set contains all limit points of Cauchy sequences. which are very similar to cluster points.

My question is: in a metric space and a closed interval (usual topology) is it possible to have points clustering without a cluster point?

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

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

# Is every Closed set a complete space?

Loading...

Similar Threads - every Closed complete | Date |
---|---|

I Proof that retract of Hausdorff space is closed | Oct 8, 2017 |

Every nonnegative real has an nth root proof | Feb 8, 2015 |

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

Every bounded sequence is Cauchy? | Nov 2, 2014 |

Understanding the concept of every open set being a disjoint union | Aug 25, 2013 |

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