reserve i for Integer,
  a, b, r, s for Real;

theorem Th5:
  for T being non empty TopSpace, Z being non empty SubSpace of T,
  t being Point of T, z being Point of Z, N being open a_neighborhood of t, M
being Subset of Z st t = z & M = N /\ [#]Z holds M is open a_neighborhood of z
proof
  let T be non empty TopSpace, Z be non empty SubSpace of T, t be Point of T,
  z be Point of Z, N be open a_neighborhood of t, M be Subset of Z such that
A1: t = z and
A2: M = N /\ [#]Z;
  M is open by A2,TOPS_2:24;
  then
A3: Int M = M by TOPS_1:23;
  t in Int N & Int N c= N by CONNSP_2:def 1,TOPS_1:16;
  then z in Int M by A1,A2,A3,XBOOLE_0:def 4;
  hence thesis by A2,CONNSP_2:def 1,TOPS_2:24;
end;
