reserve e,u for set;
reserve X, Y for non empty TopSpace;

theorem Th3:
  for W being Point of Y, A being continuous Function of X,Y, G
  being a_neighborhood of W holds A"G is a_neighborhood of A"{W}
proof
  let W be Point of Y, A be continuous Function of X,Y, G be a_neighborhood of
  W;
  W in Int G by CONNSP_2:def 1;
  then {W} c= Int G by ZFMISC_1:31;
  then
A1: A"{W} c= A"Int G by RELAT_1:143;
  A"Int G c= Int(A"G) by Th2;
  hence A"{W} c= Int(A"G) by A1;
end;
