theorem Th14:
  for P being Subset of TOP-REAL 2, s1 st
  P= { |[s,r]| where s,r is Real: s <= s1 }
  holds P is closed
proof
  let P be Subset of TOP-REAL 2, s1;
  reconsider P1= { |[s,r]| where s,r is Real : s > s1 }
  as Subset of TOP-REAL 2 by Lm10;
  assume P= { |[s,r]| where s,r is Real: s <= s1 };
  then
A1: P=P1` by Th11;
  P1 is open by JORDAN1:20;
  hence thesis by A1,TOPS_1:4;
end;
