on X, Let T and T' be the topology both generated by B.


T=T'

iff. T is contained in T' and T' is contained in T.

iff. for any U in T, for any x in U, there exists B' in B s.t. x in B' in U

and for any U' in T', for any x' in U', there exists B in B s.t. x' in B in U'.

by assumption, this is true.

Hence B genrates unique Topology


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