reserve n for Nat;

theorem Th11:
  for X, Y being non empty TopSpace, x being Point of X, y being
Point of Y, V being Subset of [: X, Y :] holds V is a_neighborhood of [: {x}, {
  y} :] iff V is a_neighborhood of [ x, y ]
proof
  let X, Y be non empty TopSpace, x be Point of X, y be Point of Y, V be
  Subset of [: X, Y :];
  hereby
    assume V is a_neighborhood of [: {x}, {y} :];
    then V is a_neighborhood of { [x, y] } by ZFMISC_1:29;
    hence V is a_neighborhood of [ x, y ] by CONNSP_2:8;
  end;
  assume V is a_neighborhood of [ x, y ];
  then V is a_neighborhood of { [ x, y ] } by CONNSP_2:8;
  hence thesis by ZFMISC_1:29;
end;
