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

theorem Th55:
  REAL is non boundary Subset of R^1
proof
  reconsider A = [#]REAL as Subset of R^1 by TOPMETR:17;
  [#]R^1 = REAL by TOPMETR:17;
  hence thesis;
end;
