reserve T for non empty TopSpace,
  A, B for Subset of T,
  F, G for Subset-Family of T;
reserve x for Point of T;

theorem Th55:
  A is countable implies not ex x being Point of T st x
  is_a_condensation_point_of A
proof
  assume
A1: A is countable;
  given x being Point of T such that
A2: x is_a_condensation_point_of A;
  set N = the a_neighborhood of x;
  N /\ A is not countable by A2;
  hence thesis by A1,CARD_3:94;
end;
