let X be non empty almost_discrete TopSpace; :: thesis: for a, b being Point of X holds
( Cl {a} misses Cl {b} or Cl {a} = Cl {b} )
let a, b be Point of X; :: thesis: ( Cl {a} misses Cl {b} or Cl {a} = Cl {b} )
assume (Cl {a}) /\ (Cl {b}) <> {} ; :: according to XBOOLE_0:def 7 :: thesis: 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 = 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 Cl {a} = Cl {b} by A2, Th49; :: thesis: verum