Re: a subset in X A is dense iff X intersection A is not empty

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let G be an arbitrary non empty subset of X.
I will show that G intersection A is not empty.
let g be in G which is a subset of X and therefore of cl(A) since X=cl(A)
let g be in A. then g is in G and A and therefore G intersection A is not
empty.
let g not be in A. then is g a limit point of A. therefore
(G\{g}) intersection A is not empty. but since g is not in A then this is
the same as
G intersection A is not empyt.

is it correct?


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