Does this proof work for compact Sets --Prove [0,Infinity) is not compact?
Prove S=[0,Infinity) is not compact (without observing it's not bounded).
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Let F = { A_n : n element of N } , A_n = (-1,n)
then U F = (-1,infinity) and [0,1) is a subspace of UF therefore F is an open cover of S. Let G = { a_(1k) ...a_(nk)} be a finite subspace of F and m=max( 1k...nk) then UG =(-1,m) and [0,1) is not a subspace of UG therefore S is not compact.
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Linear Mode
