reserve X for non empty TopSpace;
reserve x for Point of X;
reserve U1 for Subset of X;

theorem Th3:
  for U1 being Subset of X, x being Point of X st U1 is open & x in
  U1 holds U1 is a_neighborhood of x
proof
  let U1 be Subset of X, x be Point of X;
  assume U1 is open & x in U1;
  then x in Int U1 by TOPS_1:23;
  hence thesis by Def1;
end;
