Inductive limits of quasi locally Baire spaces

Abstract

We study quasi-locally complete locally convex spaces and generalize this concept to quasi-locally Baire locally convex spaces. It is shown that an inductive limit of strictly webbed spaces is regular if it is quasi-locally Baire. This extends Qiu's theorem on regularity. Additionally, if each step is strictly webbed and quasi-locally Baire, then the inductive limit is quasi-locally Baire if it is regular. Relevant examples are provided.