reserve Y for TopStruct;
reserve X for non empty TopSpace;

theorem Th29:
  for A being empty Subset of X holds A is discrete
proof
  let A be empty Subset of X;
  now
    let D be Subset of X;
    assume
A1: D c= A;
    now
      take G = {}X;
      thus G is open & A /\ G = D by A1;
    end;
    hence ex G being Subset of X st G is open & A /\ G = D;
  end;
  hence thesis;
end;
