English

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