Inductive limits of quasi locally Baire spaces
Functional Analysis
2021-05-14 v1 General Topology
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.
Keywords
Cite
@article{arxiv.2105.06358,
title = {Inductive limits of quasi locally Baire spaces},
author = {Thomas E. Gilsdorf},
journal= {arXiv preprint arXiv:2105.06358},
year = {2021}
}
Comments
Tentatively accepted in the Asian-European Journal of Mathematics, May, 2021