MAPPINGS FROM S(3) TO S(2) WHOSE POINT INVERSES HAVE THE SHAPE OF A CIRCLE

Let f:S(3) -> S(2) be a continuous function. If y is an element of S(2) assume that f(-1)(y) has the shape of a circle and that there are neighborhoods V subset of U of f(-1)(y) such: that for any point inverse f(-1)(z) subset of V, the inclusion of f(-1)( z) into U is essential. We show that f can be approximated arbitrarily closely by Seifert fiber maps.