An essential map theory for ${\mathcal U}_c^{\kappa}$ and PK maps

Abstract

This paper presents a continuation theory for ${\mathcal U}_c^{\kappa}$ maps. The analysis is elementary and relies on properties of retractions and fixed point theory for self maps. Also we present a separate theory for a certain subclass of ${\mathcal U}_c^{\kappa}$ maps, namely the $PK$ maps.