reserve X for non empty TopSpace;
reserve Y for non empty TopStruct;
reserve x for Point of Y;
reserve Y for non empty TopStruct;

theorem Th28:
  for x being Point of Y holds MaxADSet(x) = MaxADSet({x})
proof
  let x be Point of Y;
  set M = {MaxADSet(a) where a is Point of Y : a in {x}};
  now
    let P be set;
    assume P in M;
    then ex a being Point of Y st P = MaxADSet(a) & a in {x};
    hence P c= MaxADSet(x) by TARSKI:def 1;
  end;
  then
A1: MaxADSet({x}) c= MaxADSet(x) by ZFMISC_1:76;
  x in {x} by TARSKI:def 1;
  then MaxADSet(x) in M;
  then MaxADSet(x) c= MaxADSet({x}) by ZFMISC_1:74;
  hence thesis by A1;
end;
