
theorem Th19:
  for T being non empty TopSpace, p being Point of T, P being
  basis of p holds P is non empty
proof
  let T be non empty TopSpace, p be Point of T, P be basis of p;
  Int [#]T = [#]T by TOPS_1:15;
  then ex W being Subset of T st W in P & p in Int W & W c= [#]T by Def1;
  hence thesis;
end;
