The directional derivative

Abstract

In this chapter we shall be concerned with a function F(x, y) of two variables x and y. x is supposed to be a point of Euclidean space Rⁿ, x = (x₁, ..., x _n ), and y a point of some compact topological space y. While all the considerations of this chapter are carried out for a general y, the applications made in this book have y a closed bounded set in Euclidean space, and the reader may therefore if he wishes read “closed bounded Euclidean” when he sees “compact topological.”