reserve X for TopStruct,
  A for Subset of X;
reserve X for TopSpace,
  A,B for Subset of X;
reserve X for non empty TopSpace,
  A for Subset of X;
reserve X for TopSpace,
  A,B for Subset of X;
reserve X for non empty TopSpace,
  A, B for Subset of X;

theorem Th44:
  A is everywhere_dense & B is everywhere_dense implies A /\ B is
  everywhere_dense
proof
  assume A is everywhere_dense & B is everywhere_dense;
  then A` is nowhere_dense & B` is nowhere_dense by Th39;
  then A` \/ B` = (A /\ B)` & A` \/ B` is nowhere_dense by TOPS_1:53
,XBOOLE_1:54;
  hence thesis by Th39;
end;
