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**

# Whats an infinite intersection of open sets

Know someone interested in this topic? Share a link to this question via email,
Google+,
Twitter, or
Facebook

Have something to add?

- Similar discussions for: Whats an infinite intersection of open sets

Loading...

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