whats an infinite intersection of open sets? how is it different from finite intersection of open sets(adsbygoogle = window.adsbygoogle || []).push({});

and why is it a closed set in the case of ∞ intersection but open in case of finite. To quote kingwinner, is it being defined as a limit?

it really does look look like a limit in the case of ∞ intersections, as in the sets are tending towards their intersection but not actually attaining it . Consider the intersection of the sets

∞

π (1-1/n, 2+ 1/n)

n=1

would the smallest set be an infinitesimally small ε on either side of the closed set [1,2], which would hence be their infinite intersection?

**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!

# Whats an infinite intersection of open sets

Loading...

Similar Threads - Whats infinite intersection | Date |
---|---|

I What would it even mean to consider a "half" derivative? | Dec 21, 2017 |

B What type of figure is this? | Nov 14, 2017 |

I What is an atlas for a torus manifold? | Oct 6, 2017 |

I Gluing lemma / infinite corollary | Sep 17, 2017 |

A What defines a large gauge transformation, really? | Feb 27, 2017 |

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