Sequential retractivities and regularity on inductive limits

Abstract

In this paper we prove the following result: an inductive limit (E, t) = ind(E _n, t _n) is regular if and only if for each Mackey null sequence (x _k) in (E, t) there exists $n = n\left( {x_k } \right) \in \mathbb{N}$ such that (x _k) is contained and bounded in (E _n, t _n). From this we obtain a number of equivalent descriptions of regularity.