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.