
theorem Th2:
  for X, Y being non empty TopSpace, x being Point of X holds Y -->
  x is continuous Function of Y, X|{x}
proof
  let X, Y be non empty TopSpace, x be Point of X;
  set Z = {x};
  set f = Y --> x;
  x in Z & the carrier of (X|Z) = Z by PRE_TOPC:8,TARSKI:def 1;
  then reconsider g = f as Function of Y, X|Z by FUNCOP_1:45;
  g is continuous by TOPMETR:6;
  hence thesis;
end;
