On stratifiable locally convex spaces

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3 Citations (Scopus)

Abstract

In the present paper we prove several results on the stratifiability of locally convex spaces. In particular, we show that a free locally convex sum of an arbitrary set of stratifiable LCS is a stratifiable LCS, and that all locally convex F'-spaces whose bounded subsets are metrizable are stratifiable. Moreover, we prove that a strict inductive limit of metrizable LCS is stratifiable and establish the stratifiability of many important general and specific spaces used in functional analysis. We also construct some examples that clarify the relationship between the stratifiability and other properties.
Original languageEnglish
Pages (from-to)435-460
Number of pages26
JournalRussian Journal of Mathematical Physics
Volume6
Issue number4
Publication statusPublished - Oct 1999

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

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