"Let (X,d) be a metrix space, and let F[tex]\subset[/tex]X be closed. Define G_n to be the set of all those points x in X such that(adsbygoogle = window.adsbygoogle || []).push({});

inf { d(x,y) : y in F } < 1/n

Use these sets G_n to show that a countable intersection of open sets need not be open."

I think the quesiton meant sup { d(x,y) : y in F } < 1/n }, not inf.

Actually I don't think sup or inf should be there at all. If the question meant sup, then Gn are not necessarily open.

**Physics Forums | Science Articles, Homework Help, Discussion**

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!

# Homework Help: Open Set

**Physics Forums | Science Articles, Homework Help, Discussion**