reserve a, r, s for Real;

theorem
  for S, T being non empty TopSpace, A being Subset of S, B being Subset
of T, N being a_neighborhood of A st the TopStruct of S = the TopStruct of T &
  A = B holds N is a_neighborhood of B
proof
  let S, T be non empty TopSpace, A be Subset of S, B be Subset of T, N be
  a_neighborhood of A such that
A1: the TopStruct of S = the TopStruct of T and
A2: A = B;
  reconsider M = N as Subset of T by A1;
A3: A c= Int N by CONNSP_2:def 2;
  Int M = Int N by A1,TOPS_3:77;
  hence thesis by A2,A3,CONNSP_2:def 2;
end;
