reserve T for TopSpace,
  A, B for Subset of T;

theorem
  for A being Subset of R^1, a being Real st A = ]. -infty, a.]
  holds Int A = ]. -infty, a.[
proof
  let A be Subset of R^1, a be Real;
  assume A = ]. -infty, a.];
  then A` = ].a,+infty .[ by TOPMETR:17,XXREAL_1:224,288;
  then Cl A` = [.a,+infty .[ by BORSUK_5:49;
  then (Cl A`)` = ]. -infty, a.[ by TOPMETR:17,XXREAL_1:224,294;
  hence thesis by TOPS_1:def 1;
end;
