Baire properties of (LF)-spaces
Abstract
We relate the study of (LF)–spaces with some covering properties of locally convex spaces, which are variations of the theme of "Baire Space". All (LF)-spaces are partitioned into theree classes, called
,
and
-spaces respectively. We then show that these classes are precisely the classes of
-spaces that distinguish between the several Baire-type coverings we considered.The role of the sequence space φ in this context is studied.The interaction between
-spaces and the Separable Quotient Problem is also discussed.
![(LF)<sub>1</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/3a579e7f6b9067b2c77031fc5b832b12.png)
![(LF)<sub>2</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/dd50a1d25ea03e50df4d5d06cfc1052e.png)
![(LF)<sub>3</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/e0a25cef5f3c8b3b300eaf29eb5562ce.png)
![(LF)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/a48a5b1013c7e2986d531ea0661df1df.png)
![(LF)<sub>3</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/e0a25cef5f3c8b3b300eaf29eb5562ce.png)
DOI Code:
10.1285/i15900932v7n1p1
Full Text: PDF