- #1

joypav

- 151

- 0

Let's call the set F.

I've been thinking about this problem for a little bit, and it just doesn't seem like I have enough initial information!

I tried listing some things that I know about closed sets in R:

$\cdot$ Countable dense subset is the same as being separable (I think?)

$\cdot$ F contains all of it's limit points

$\cdot$ Every cauchy sequence in F converges to a point in F

$\cdot$ If F is closed then F is $G_\delta$, a countable intersection of open sets (I thought this may be helpful because the sets are countable?)

I considered somehow utilizing the rational numbers, because they are dense in R, and for each x in F having a sequence of rational numbers that converges to x. However, this was just an idea.

Obviously I haven't done much concrete work on it. But I would appreciate a push in the right direction!