theorem Th25: :: TEX_1:25

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 Subset of Y holds
( ( A c= D \ {d0} implies A is open ) & ( A <> D & A is open implies A c= D \ {d0} ) ) ) ) )