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 Th49:
  for p being Point of T st p is_a_condensation_point_of A holds p
  is_an_accumulation_point_of A
proof
  let p be Point of T;
  assume
A1: p is_a_condensation_point_of A;
  for U being open Subset of T st p in U ex q being Point of T st q <> p &
  q in A & q in U
  proof
    let U be open Subset of T;
    assume p in U;
    then reconsider N = U as a_neighborhood of p by CONNSP_2:3;
    reconsider NU = N /\ A as non empty non countable set by A1;
    consider q being Element of NU such that
A2: p <> q by SUBSET_1:50;
    q in NU;
    then reconsider q as Point of T;
    q in A & q in U by XBOOLE_0:def 4;
    hence thesis by A2;
  end;
  hence thesis by TOPGEN_1:21;
end;
