for S1, S2, T1, T2 being non empty TopSpace
for R being Refinement of [:S1,T1:],[:S2,T2:] st the carrier of S1 = the carrier of S2 & the carrier of T1 = the carrier of T2 holds
{ ([:U1,V1:] /\ [:U2,V2:]) where U1 is Subset of S1, U2 is Subset of S2, V1 is Subset of T1, V2 is Subset of T2 : ( U1 is open & U2 is open & V1 is open & V2 is open ) } is Basis of R