theorem Th20:
  Closed-Interval-TSpace(0,1) = I[01]
proof
  reconsider P = [.0,1.] as Subset of R^1;
  set TR = TopSpaceMetr(RealSpace);
  reconsider P9 = P as Subset of TR;
  thus Closed-Interval-TSpace(0,1) = TR|P9 by Th19
    .= I[01] by BORSUK_1:def 13;
end;
