reserve T for non empty TopSpace,
  A, B for Subset of T,
  F, G for Subset-Family of T,
  x for set;

theorem Th53:
  RAT is boundary Subset of R^1
proof
  B` is dense by Th52,BORSUK_5:def 1,TOPMETR:17;
  hence thesis by TOPS_1:def 4;
end;
