for X1, X2 being TopSpace
for D1 being Subset of X1
for D2 being Subset of X2 st D1 = D2 & TopStruct(# the carrier of X1, the topology of X1 #) = TopStruct(# the carrier of X2, the topology of X2 #) & D1 is closed holds
D2 is closed by Th76;