Related papers: The category of Silva spaces is not integral

Countable projective limits of countable inductive limits, called PLB-spaces, of weighted Banach spaces of continuous functions have recently been investigated by Agethen, Bierstedt and Bonet. We extend their investigation to the case of…

We consider special subclasses of the class of Lindel\"of Sigma-spaces obtained by imposing restrictions on the weight of the elements of compact covers that admit countable networks: A space $X$ is in the class $L\Sigma(\leq\kappa)$ if it…

Countable projective limits of countable inductive limits, called PLB-spaces, of weighted Banach spaces of continuous functions have recently been investigated by Agethen, Bierstedt and Bonet. In a previous article, the author extended…

In a locally $\lambda$-presentable category, with $\lambda$ a regular cardinal, classes of objects that are injective with respect to a family of morphisms whose domains and codomains are $\lambda$-presentable, are known to be characterized…

We extend the theory of the Lusternik-Schnirelmann category to general metric spaces by means of covers by arbitrary subsets. We also generalize the definition of the strict category weight. We show that if the Bockstein homomorphism on a…

In this article we propose a conception of mixed limits of functional spaces as the case, when the upper limit (projective limit of inductive limits) and the lower limit (inductive limit of projective limits) coincide as topological spaces,…

We consider the compact spaces sigma_n(I) of subsets of an uncountable set I of cardinality at most n and their countable products. We give a complete classification of their Banach spaces of continuous functions and a partial topological…

Many of the known complemented subspaces of L_p have realizations as sequence spaces. In this paper a systematic approach to defining these spaces which uses partitions and weights is introduced. This approach gives a unified description of…

The class of $L\Sigma(\leq\omega)$-spaces was introduced in 2006 by Kubi\'s, Okunev and Szeptycki as a natural refinement of the classical and important notion of Lindel\"of $\Sigma$-spaces. Compact $L\Sigma(\leq\omega)$-spaces were…

We determine the Lusternik-Schnirelmann category of the projective product spaces introduced by D. Davis. We also obtained an upper bound for the topological complexity of these spaces, which improves the estimate given by J. Gonz\'alez, M.…

Countable projective limits of countable inductive limits, so-called PLB-spaces, of weighted Banach spaces of continuous functions have recently been investigated by Agethen, Bierstedt and Bonet, who analyzed locally convex properties in…

It is proved that there exist complemented subspaces of countable topological products (locally convex direct sums) of Banach spaces which cannot be represented as topological products (locally convex direct sums) of Banach spaces. (This is…

This paper considers coorbit spaces parametrized by mixed, weighted Lebesgue spaces with respect to the quasi-regular representation of the semi-direct product of Euclidean space and a suitable matrix dilation group. The class of dilation…

Menger's conjecture that Menger spaces are /sigma-compact is false; it is true for analytic subspaces of Polish spaces and undecidable for more complex definable subspaces of Polish spaces. For non-metrizable spaces, analytic Menger spaces…

In this work we shall be concerned with some stability aspects of the classical problem of extension of $C(K)$-valued operators. We introduce the class $\mathscr{LP}$ of Banach spaces of Lindenstrauss-Pe{\l}czy\'{n}ski type as those such…

We consider the homotopy category of complexes of projective modules over any gentle algebra. We prove that indecomposable $\Sigma$-pure-injective objects in s must be shifts of string or band complexes. We begin with a survey of purity in…

The category $Ban$ of Banach spaces and linear maps of norm $\leq 1$ is locally $\aleph_1$-presentable but not locally finitely presentable. We prove, however, that $Ban$ is locally finitely presentable in the enriched sense over complete…

We examine locally compact normal spaces in models of form PFA(S)[S], in particular characterizing paracompact, countably tight ones as those which include no perfect pre-image of omega_1 and in which all separable closed subspaces are…

We investigate several categories of integrable $sl(\infty)$-, $o(\infty)$-, $sp(\infty)$-modules. In particular, we prove that the category of integrable $sl(\infty)$-, $o(\infty)$-, $sp(\infty)$-modules with finite-dimensional weight…

Stefanich generalized the notion of (locally) presentable $(\infty, 1)$-category to the notion of presentable $(\infty, n)$-category. We give a new description based on the new notion of $\kappa$-compactly generated $(\infty, n)$-category,…