We discuss relationships in Lindelöf spaces among the properties “Menger”, “Hurewicz”, “Alster”, “productive”, and “D”. This note is a continuation of [13]. The question of what additional assumptions ensure that the product of two Lindelöf spaces is Lindelöf is natural and well-studied. See e.g., [28], [30], [2], [3], [4], [5], [6], [32], [33]. D-spaces were introduced in [20]. Definition. A s...

We consider the cardinal invariant CG(X) of the minimal number of weakly compact subsets which generate a Banach space X. We study the behavior of this index when passing to subspaces, its relation with the Lindelöf number in the weak topology and other related questions. A Banach space is weakly compactly generated if there is a weakly compact subset which is linearly dense and weakly Lindelöf...

We introduce notions of nearly good relations and N-sticky modulo a relation as tools for proving that spaces are D-spaces. As a corollary to general results about such relations, we show that Cp(X) is hereditarily a D-space whenever X is a Lindelöf Σ-space. This answers a question of Matveev, and improves a result of Buzyakova, who proved the same result for X compact. We also prove that if a ...

this paper deals with the behavior at infinity of solutions to a class of wave equations with nonlinear dampingterms defined in a semi-infinite cylinder. the spatial behavior of solutions is studied and an alternative ofphragmén-lindelöf type theorems is obtained in the results. the main point in the contribution is the use of energy method.

The stability of the Lindelöf property under the formation of products and of sums is investigated in ZF (= Zermelo-Fraenkel set theory without AC, the axiom of choice). It is • not surprising that countable summability of the Lindelöf property requires some weak choice principle, • highly surprising, however, that productivity of the Lindelöf property is guaranteed by a drastic failure of AC, ...

A topological space X is a ΣΣ∗-space provided for every sequence 〈fn〉n=0 of continuous functions from X to R, if the series ∑∞ n=0 |fn| converges pointwise then it converges pseudo-normally. We show that every regular Lindelöf ΣΣ∗-space has Rothberger property. We also construct, under the continuum hypothesis, a ΣΣ∗-subset of R of cardinality continuum.

We continue our examination of absolute CR -epic spaces, or spaces with the property that any embedding induces an epimorphism, in the category of commutative rings, between their rings of continuous functions. We examine more closely the deleted plank construction, which generalizes the Dieudonné construction, and yields absolute CR -epic spaces which are not Lindelöf. For the Lindelöf case, a...