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

theorem Th6:
  for x being Point of Y holds {x} is anti-discrete
proof
  let x be Point of Y;
  now
    let G be Subset of Y such that
    G is open;
    assume {x} meets G;
    then consider a being object such that
A1: a in {x} /\ G by XBOOLE_0:4;
    a in {x} by A1,XBOOLE_0:def 4;
    then
A2: a = x by TARSKI:def 1;
    a in G by A1,XBOOLE_0:def 4;
    hence {x} c= G by A2,ZFMISC_1:31;
  end;
  hence thesis;
end;
