Source: wikibot/birkhoff-kellogg-invariant-direction-theorem
= Birkhoff–Kellogg invariant-direction theorem
{wiki=Birkhoff–Kellogg_invariant-direction_theorem}
The Birkhoff–Kellogg invariant-direction theorem is a result in the field of topology and fixed-point theory, specifically in the study of continuous functions on convex sets. The theorem addresses the behavior of continuous functions defined on convex subsets of a Euclidean space.