for X, Y being non empty TopSpace
for D being Subset of [:X,Y:] st D is open holds
for X1 being Subset of X
for Y1 being Subset of Y holds
( ( X1 = (pr1 ( the carrier of X, the carrier of Y)) .: D implies X1 is open ) & ( Y1 = (pr2 ( the carrier of X, the carrier of Y)) .: D implies Y1 is open ) )