theorem Th53:
  for G being UnContinuous TopaddGroup, a being Point of G, A being
  a_neighborhood of a holds -A is a_neighborhood of -a
proof
  let G be UnContinuous TopaddGroup, a be Point of G, A be a_neighborhood of a;
  a in Int A by CONNSP_2:def 1;
  then consider Q being Subset of G such that
A1: Q is open and
A2: Q c= A & a in Q by TOPS_1:22;
  -Q c= -A & -a in -Q by A2,ThB8;
  hence -a in Int (-A) by A1,TOPS_1:22;
end;
