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{x} cluster points


Active member
Mar 1, 2012
Is it correct that the cluster points of the {x} in any topology T at X is empty ?

My work:

(X,T), topology let x in X
suppose there exist a in {x}'
that means for all open set U and x in U

$U\{x} \hat {x} $ is not empty but the only element in {x} is x so the intersection will be x which contradict with U\{x}
so {x}' is empty, is it correct ?