Abstract:

Everybody meets multivalued maps very early in his mathematical education, as inverses of maps which are not onetoone, but in elementary lectures the multivalued aspect is usually suppressed by means of elementary tricks or restrictions which make sense for practical purposes; think of [see pdf for notation] which has the inverse[see pdf for notation], from [see pdf for notation] (the subsets of R); or think of a linear operator [see pdf for notation] with kernel [see pdf for notation]; in which case one uses the trick to consider [see pdf for notation], defined by [see pdf for notation] which is onetoone and therefore has a singlevalued inverse [see pdf for notation]. 