
theorem Th18:
  for T being TopStruct, p being Point of T holds bool the carrier
  of T is basis of p
proof
  let T be TopStruct, p be Point of T;
  reconsider F = bool the carrier of T as Subset-Family of T;
  reconsider F as Subset-Family of T;
  F is basis of p
  proof
    let A be Subset of T such that
A1: p in Int A;
    take Int A;
    thus thesis by A1,TOPS_1:16;
  end;
  hence thesis;
end;
