theorem :: TEX_1:26

for D being non empty set
for d0 being Element of D
for Y being non empty TopSpace holds
( TopStruct(# the carrier of Y, the topology of Y #) = TopStruct(# the carrier of (STS (D,d0)), the topology of (STS (D,d0)) #) iff ( the carrier of Y = D & ( for A being non empty Subset of Y holds Cl A = A \/ {d0} ) ) )