When separability of the space of ultra-extremal functions is preserved

Abstract

The ultrametrically injective hull T_X of an ultrametric space (X,d) is investigated by viewing it as the space of ultra-extremal functions over X. It turns out that the ultra-extremal functions are also ultra-Katětov functions, satisfying two inequalities derived from the strong triangle inequality. We shall compare the ultra-extremal functions with some classes of functions dened with the help of one of the two inequalities from the definition of ultra-Katětov functions. We shall consider the question of when separability of the space of ultra-extremal functions is preserved.

Mathematics Subject Classification (2010): Primary 47H09; Secondary 54E35, 54C15
54E55.

Keywords: Separability, dense, ultra-extremal, ultrametrically injective, ultra-Katětov functions, ultrametric uniform convergence, pointwise convergence