reconsider A = P, B = Q as Subset of T ;
A1: B is open by PRE_TOPC:def 5;
A is open by PRE_TOPC:def 5;
then P \/ Q is open by A1, TOPS_1:37;
hence P \/ Q is Element of Topology_of T by PRE_TOPC:def 5; :: thesis: verum