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

theorem
  for A being Subset of R^1, a being Real st A = [.a,+infty .[
  holds Int A = ].a,+infty .[
proof
  let A be Subset of R^1, a be Real;
  assume A = [.a,+infty .[;
  then A` = ]. -infty,a.[ by TOPMETR:17,XXREAL_1:224,294;
  then Cl A` = ]. -infty,a.] by BORSUK_5:51;
  then (Cl A`)` = ].a,+infty .[ by TOPMETR:17,XXREAL_1:224,288;
  hence thesis by TOPS_1:def 1;
end;
