
theorem Th6:
  for T being non empty TopSpace, A being Subset of T st A is open
  holds for p,q being Point of T holds p in A & (T_0-canonical_map(T)).p = (
  T_0-canonical_map(T)).q implies q in A
proof
  let T be non empty TopSpace;
  let A be Subset of T such that
A1: A is open;
  set F=T_0-canonical_map(T);
  let p,q be Point of T;
  assume that
A2: p in A and
A3: F.p = F.q;
A4: F.p = Class(Indiscernibility(T),p) by Th4;
  q in F.p by A3,BORSUK_1:28;
  then [q,p] in Indiscernibility(T) by A4,EQREL_1:19;
  hence thesis by A1,A2,Def3;
end;
