Baire properties of (LF)-spaces


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 (LF)<sub>1</sub>, (LF)<sub>2</sub> and (LF)<sub>3</sub>-spaces respectively. We then show that these classes are precisely the classes of (LF)-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 (LF)<sub>3</sub>-spaces and the Separable Quotient Problem is also discussed.

DOI Code: 10.1285/i15900932v7n1p1

Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.