I'm not very good at topology but am reviewing it for the GRE Subject Test. Here's a question that I think I know, but would like to check with you guys.(adsbygoogle = window.adsbygoogle || []).push({});

We define:

E_{k}= B(0, k) - B(0, k-1), where B(0,k) is an open ball around the origin with diameter k. Now suppose that T_{k}is a subset of E_{k}for all k, where T is compact. Now let K be the union (1 to infinity) of all T_{k}. Is K open or closed?

I say closed, but I'm not sure.

**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!

# Closed or Open?

Loading...

Similar Threads - Closed Open | Date |
---|---|

Open and closed | May 27, 2010 |

When to use open/closed set,etc | Apr 12, 2010 |

Topology Open and Closed Sets | Jan 20, 2010 |

Closed/Open Transition Function Question | Jan 14, 2010 |

If a set A is both open and closed then it is R(set of real numbers) | Sep 10, 2009 |

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