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 Th30:
  A is nowhere_dense & B is boundary implies A \/ B is boundary
proof
  assume A is nowhere_dense;
  then
A1: Cl A is boundary;
  assume B is boundary;
  then A c= Cl A & B \/ Cl A is boundary by A1,PRE_TOPC:18,TOPS_1:49;
  hence thesis by Th11,XBOOLE_1:9;
end;
