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## Homework Statement

R>0, let K be a closed subset of C such that K [tex]\subset[/tex] B

_{R}(0) (so K is compact). Show that there exists 0 < r < R such that K[tex]\subset[/tex] Br(0).

## Homework Equations

## The Attempt at a Solution

Can I write B

_{R}(0) = {x[tex]\in[/tex]C : d(x,0) [tex]\leq[/tex]R}?

I know that a compact set is closed and bounded.

Is it something to do with us using [tex]\subset[/tex] and not [tex]\subseteq[/tex]?

As if it was [tex]\subseteq[/tex] then maybe K = B

_{R}(0) then there wouldn't be an r. But as K is strictly contained in the ball there must be a bit of room for manoeuvre.

These are my thoughts on this problem. I'm not sure if they're correct or what the question is asking, and if they are I don't know how to write them more formally?

Thank you :)