reserve r for Real;
reserve a, b for Real;
reserve T for non empty TopSpace;
reserve A for non empty SubSpace of T;
reserve P,Q for Subset of T,
  p for Point of T;
reserve M for non empty MetrSpace,
  p for Point of M;
reserve A for non empty SubSpace of M;
reserve F,G for Subset-Family of M;

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;
