RETURN NEXT in Postgres Function
If the results are not meant to be used in a subquery but by code, you may use a REFCURSOR in a transaction.

Example:

CREATE FUNCTION example_cursor() RETURNS refcursor AS $$
DECLARE
  c refcursor;
BEGIN
  c:='mycursorname';
  OPEN c FOR select * from generate_series(1,100000);
  return c;                                       
end;
$$ language plpgsql;


Usage for the caller:

BEGIN;
SELECT example_cursor();
 [output: mycursor]
FETCH 10 FROM mycursor;

 Output:

 generate_series 
-----------------
               1
               2
               3
               4
               5
               6
               7
               8
               9
              10

CLOSE mycursor;
END;


When not interested in piecemeal retrieval, FETCH ALL FROM cursorname may also be used to stream all results to the caller in one step.