reserve a, r, s for Real;

theorem Th8:
  for S, T being non empty TopSpace, s being Point of S, t being
  Point of T, A being a_neighborhood of s st the TopStruct of S = the TopStruct
  of T & s = t holds A is a_neighborhood of t
proof
  let S, T be non empty TopSpace, s be Point of S, t be Point of T, A be
  a_neighborhood of s such that
A1: the TopStruct of S = the TopStruct of T and
A2: s = t;
  reconsider B = A as Subset of T by A1;
A3: s in Int A by CONNSP_2:def 1;
  Int A = Int B by A1,TOPS_3:77;
  hence thesis by A2,A3,CONNSP_2:def 1;
end;
