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

theorem Th34:
  for XX being non empty TopSpace, X being non empty SubSpace of
  XX, D being non empty a_partition of the carrier of X, W being Point of XX st
  not W in the carrier of X holds Proj TrivExt D.W = {W}
proof
  let XX be non empty TopSpace, X be non empty SubSpace of XX, D be non empty
  a_partition of the carrier of X, W be Point of XX;
  assume not W in the carrier of X;
  then W in {W} & {W} in TrivExt D by Th32,TARSKI:def 1;
  hence thesis by EQREL_1:65;
end;
