reserve
  X for non empty set,
  FX for Filter of X,
  SFX for Subset-Family of X;

theorem
  for T being non empty TopSpace,x being Point of T holds
  NeighborhoodSystem x is filter_base of [#]T
  proof
    let T be non empty TopSpace, x be Point of T;
    reconsider Nx=NeighborhoodSystem x as Filter of [#]T by Th36;
    Nx is basis of Nx by Th03;
    hence thesis by Th09;
  end;
