Multis

Abstract

The multis considered in this chapter are harmless compared with their namesakes in daily life, since they are just multivalued maps, also called set-valued or multiple-valued maps. You meet them at an early stage as inverses of maps which are not one-to-one, though the multivalued aspect is usually suppressed in elementary courses. Think of complex function theory, where you just choose one branch of the logarithm or the n-th root for practical purposes before, perhaps, you study analytic continuation, or think of linear operator theory, where you just factor out the kernel of T∈L(X, Y) so that you have a nice inverse ${\hat T^{ - 1}}:R\left( T \right) \to X/N\left( T \right)$ as in the proof of Proposition 7.9, or, since three is lucky, think of elementary differentiability where you either have a unique tangent (plane) or ‘nothing’.

Taboos, though forbidden, propagate dreadfully.

Stanislaw Jerzy Lec

Obviousness is always the enemy of correctness. Hence we must invent a new and difficult symbolism in which nothing is obvious.

Bertrand Russell