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 Th17:
  A is dense implies A <> {}
proof
  assume A is dense;
  then
A1: Cl A = [#]X;
  assume A = {};
  hence contradiction by A1,PRE_TOPC:22;
end;
