\(\kappa\)-to-1 Darboux-Like Functions

Abstract

We examine the existence of \(\kappa\)-to-1 functions \(f\colon\mathbb{R}\to\mathbb{R}\) in the class of continuous functions, Darboux functions, functions with perfect roads, and functions with the Cantor intermediate value property. In this setting \(\kappa\) denotes a cardinal number (finite or infinite). We also consider different variations on this theme.