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
  for a,b being Real, B being Subset of I[01] st 0<=a & a<=b & b
  <=1 & B=[.a,b.] holds Closed-Interval-TSpace(a,b)=I[01]|B by Th20,Th23;
