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

theorem Th20:
  F = { A } implies (A is closed iff F is closed)
proof
  assume
A1: F = { A };
  hereby
    assume A is closed;
    then for A being Subset of T st A in F holds A is closed by A1,TARSKI:def 1
;
    hence F is closed by TOPS_2:def 2;
  end;
  assume
A2: F is closed;
  A in F by A1,TARSKI:def 1;
  hence thesis by A2,TOPS_2:def 2;
end;
