### 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 language | English |
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Pages (from-to) | 435-460 |

Number of pages | 26 |

Journal | Russian Journal of Mathematical Physics |

Volume | 6 |

Issue number | 4 |

Publication status | Published - Oct 1999 |

### ASJC Scopus subject areas

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

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## Cite this

Shkarin, S. (1999). On stratifiable locally convex spaces.

*Russian Journal of Mathematical Physics*,*6*(4), 435-460.