
theorem Th15:
  for S, T being TopSpace, A being closed Subset of S, B being
  closed Subset of T holds [:A,B:] is closed
proof
  let S, T be TopSpace;
  let A be closed Subset of S;
  let B be closed Subset of T;
  Cl A = A & Cl [:A,B:] = [:Cl A,Cl B:] by Th14,PRE_TOPC:22;
  hence thesis by PRE_TOPC:22;
end;
