reserve S, R for 1-sorted,
  X for Subset of R,
  T for TopStruct,
  x for set;
reserve H for non empty multMagma,
  P, Q, P1, Q1 for Subset of H,
  h for Element of H;
reserve G for Group,
  A, B for Subset of G,
  a for Element of G;

theorem
  for T being homogeneous non empty TopSpace st ex p being Point of T st
  {p} is closed holds T is T_1
proof
  let T be homogeneous non empty TopSpace;
  given p being Point of T such that
A1: {p} is closed;
  now
    let q be Point of T;
    consider f being Homeomorphism of T such that
A2: f.p = q by Def6;
    dom f = the carrier of T by FUNCT_2:def 1;
    then Im(f,p) = {f.p} by FUNCT_1:59;
    hence {q} is closed by A1,A2,TOPS_2:58;
  end;
  hence thesis by URYSOHN1:19;
end;
