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 Th56:
  A is countable implies A^0 = {}
proof
  assume
A1: A is countable;
  assume A^0 <> {};
  then consider x being object such that
A2: x in A^0 by XBOOLE_0:def 1;
  reconsider x9 = x as Point of T by A2;
  x9 is_a_condensation_point_of A by A2,Def10;
  hence thesis by A1,Th55;
end;
