On properly separable quotients of strict (LF) Spaces

Journal of the Australian Mathematical Society

W. J. Robertson¹ 

关键词: 46 A 05;    46 A 07;    46 A 12;   

DOI  :  10.1017/S1446788700031736

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

All known Banach spaces have an infinite-dimensional separable quotient and so do all nonnormable Fréchet spaces, although the general question for Banach spaces is still open. A properly separable topological vector space is defined, in such a way that separable and properly separable are equivalent for an infinite-dimensional complete metrisable space. The main result of this paper is that the strict inductive limit of a sequence of non-normable Fréchet spaces has a properly separable quotient.

【 授权许可】

Unknown