- #1
Mathsgirl
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Homework Statement
R>0, let K be a closed subset of C such that K [tex]\subset[/tex] BR(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 BR(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 = BR(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 :)