We have two closed sets A,B in R^n. Does A+B= {x+y | x is an element of A, y is an element of B} have to be closed?(adsbygoogle = window.adsbygoogle || []).push({});

I know that both the union and intersection of two closed sets have to be closed. I'm guessing from the question that the answer is no, but I've been playing around with different intervals or R^2 sets that could represent A and B and can't come up with any counterexample to show that A+B need not be closed.

Thanks for any help you can offer!

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

Dismiss Notice

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!

# Is a sum of closed sets closed?

Loading...

Similar Threads - closed sets closed | Date |
---|---|

B Can open sets be described in-terms of closed sets? | Apr 9, 2016 |

Sum of two closed sets are measurable | Mar 25, 2012 |

Set of integers is closed. | Dec 11, 2011 |

Phase space, open closed set | Sep 5, 2011 |

Closed sets in Cantor Space that are not Clopen | Aug 5, 2011 |

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