Extensions of contractions and uniform contractions on dense subspaces

Abstract

We give two extension theorems, which state conditions under which a (uniform) contraction from a dense subspace of a convergence approach space (approach uniform convergence space) to a convergence approach space (approach uniform convergence space) can be extended to a (uniform) contraction de ned on the whole space. In order to derive these extension theorems we de ne and study certain diagonal axioms and the concept of uniform regularity for approach uniform convergence spaces.

Keywords: Convergence approach space, approach uniform convergence space, diagonal condition, neighbourhoods, neighbourhood condition, regularity, uniform regularity, extension of mappings

Quaestiones Mathematicae 37(2014), 111-125