# Every open subset of R^p is the union of countable collection of

1. Sep 1, 2014

### vish_maths

Every open sub set of Rp is the union of countable collection of closed sets.

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2. Sep 1, 2014

### micromass

Staff Emeritus
Take an irrational number $a$ in $G$. You can find a certain open ball $B(a,\varepsilon)$ which remains in $G$. What can you tell about the rational numbers in that ball? In particular, if $q\in B(a,\varepsilon)$ is rational, what can you tell about the closed set in the hint?

3. Sep 1, 2014

### WWGD

This is equivalent to R^p being 2nd-countable.

4. Sep 2, 2014