Inductive limits of quasi-locally Baire spaces

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Abstract

Quasi-locally complete locally convex spaces are generalized 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. Distinguishing examples are provided.

Original languageEnglish
Article number2250074
JournalAsian-European Journal of Mathematics
Volume15
Issue number4
DOIs
StatePublished - Apr 1 2022

Keywords

  • Quasi-locally complete
  • inductive limit
  • quasi-locally Baire

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