reserve Y for TopStruct;
reserve X for non empty TopSpace;
reserve X for almost_discrete non empty TopSpace;

theorem Th50:
  for a, b being Point of X holds Cl {a} misses Cl {b} or Cl {a} = Cl {b}
proof
  let a, b be Point of X;
  assume Cl {a} /\ Cl {b} <> {};
  then consider x being object such that
A1: x in Cl {a} /\ Cl {b} by XBOOLE_0:def 1;
  reconsider x as Point of X by A1;
  x in Cl {a} by A1,XBOOLE_0:def 4;
  then
A2: Cl {x} = Cl {a} by Th49;
  x in Cl {b} by A1,XBOOLE_0:def 4;
  hence thesis by A2,Th49;
end;
