reserve Y for TopStruct;

theorem Th26:
  for A being Subset of Y holds A is discrete implies for x being
  Point of Y st x in A ex G being Subset of Y st G is open & A /\ G = {x}
proof
  let A be Subset of Y;
  assume
A1: A is discrete;
  let x be Point of Y;
  assume
A2: x in A;
  then reconsider Y9 = Y as non empty TopStruct;
  reconsider B = {x} as Subset of Y9 by ZFMISC_1:31;
  reconsider A9 = A as Subset of Y9;
  {x} c= A9 by A2,ZFMISC_1:31;
  then consider G being Subset of Y9 such that
A3: G is open and
A4: A9 /\ G = B by A1;
  reconsider G as Subset of Y;
  take G;
  thus thesis by A3,A4;
end;
