We show that when a linear quotient map to a separable Banach space X has a Lipschitz
right inverse, then it has a linear right inverse. If a separable space X embeds isometrically …

Generally following Horv~, th [7], we say that a rare (nowhere dense) subset of a topological
space is one whose closure has an empty interior. A Baire space is a topological space in …

fragmentability in the sense of Jayne and Rogers and its natural uniform generalizations
play a major role in this paper. Our applications show that problems concerning the …

Since Tychonoff spaces X serve as continuous Hamel bases for the strong dual L β X of C p
X, an old splitting theorem proves: C p X is distinguished⇔ L β X has the strongest locally …

The existence of metrizable (LF)-spaces was announced by Stephen A. Saxon (“Metrizable
generalized (LF)-spaces”, 701–46–14), in Notices Amer. Math. Soc. 20 (1973), A–143 …

By a variety of topological algebras we mean a class V of topological algebras of a fixed type
closed under the formation of subalgebras, products and quotients (ie images under …

We start the systematic study of Fréchet spaces which are ℵ-spaces in the weak topology. A
topological space X is an ℵ 0-space or an ℵ-space if X has a countable k-network or a σ …

The quotient problem has a positive solution for the weak and strong duals of $ C_ {c}\left
(X\right) $($ X $ an infinite Tichonov space), for Banach spaces $ C_ {c}\left (X\right) $, and …

Motivated by Rosenthal's famous l 1-dichotomy in Banach spaces, Haydon's theorem, and
additionally by recent works on tame dynamical systems, we introduce the class of tame …

Recently several papers on varieties of topological groups have appeared. In this note we
investigate the question: if Ω is a class of topological groups, what topological groups are in …