You will obtain the result from the existence of an open subset in containing such that . But if such an open set does not exist, we would have a contradiction with .
let A be a subset of a space (X,T) and let A' is the derive set (the set that contains the clusters points ) show that {y} is open in the subspace
I will try to show that A-{y} is closed by prove that
(y)={y} is in not in (X,T) and it is enough to prove that
Suppose that
but
so
here where I stuck can anyone help me ??
Thanks