Related papers: Internal characterizations of productively Lindel\…
The class of spaces such that their product with every Lindel\"of space is Lindel\"of is not well-understood. We prove a number of new results concerning such productively Lindel\"of spaces with some extra property, mainly assuming the…
No convenient internal characterization of spaces that are productively Lindelof is known. Perhaps the best general result known is Alster's internal characterization, under the Continuum Hypothesis, of productively Lindelof spaces which…
Michael asked whether every productively Lindel\"of space is powerfully Lindel\"of. Building of work of Alster and De la Vega, assuming the Continuum Hypothesis, we show that every productively Lindel\"of space of countable tightness is…
We prove that under certain set-theoretic assumptions every productively Lindel\"of space has the Hurewicz covering property, thus improving upon some earlier results of Aurichi and Tall.
For a Tychonoff space $X$ and a family $\lambda$ of subsets of $X$, we denote by $C_{\lambda}(X)$ the $T_1$-space of all real-valued continuous functions on $X$ with the $\lambda$ -open topology. A topological space is productively…
We discuss relationships in Lindelof spaces among the properties "indestructible", "productive", "D", and related properties.
There has recently been considerable interest in productively Lindelof spaces, i.e. spaces such that their product with every Lindelof space is Lindelof. Here we make several related remarks about such spaces. Indestructible Lindelof…
In this paper we present a new characterization of inner product spaces related to the p-angular distance. We also generalize some results due to Dunkl, Williams, Kirk, Smiley and Al-Rashed by using the notion of p-angular distance.
Lindel\"of spaces are studied in any basic Topology course. However, there are other interesting covering properties with similar behaviour, such as almost Lindel\"of, weakly Lindel\"of, and quasi-Lindel\"of, that have been considered in…
We prove that assuming $\mathfrak{b}=\mathfrak{d}$, in the class of hereditarily Lindel\"of spaces, each productively Scheepers space is productively Hurewicz. The above statement remains true in the class of all general topological spaces…
In this paper we study the properties of P-generated spaces (by analogy with compactly generated). We prove that a regular Lindel\"of generated space with uncountable dispersion character is resolvable. It is proved that Hausdorff…
This article is devoted to the interplay between productively Menger and productively Hurewicz subspaces of the Cantor space. In particular, we show that in the Laver model for the consistency of the Borel's conjecture these two notions…
In this paper we introduce and study the local version of the Menger property, namely locally Menger property (or, locally Menger space). We explore some preservation like properties in this space. We also discuss certain situations where…
The quasi-Lindel\"of property was first introduced by Arhangelski in \cite{Arc}, as a strengthening of the weakly Lindel\"of property. However, unlike Lindel\"of and weakly Lindel\"of spaces, very little is known about how quasi-Lindel\"of…
We investigate preservation of the Lindel\"of property of topological spaces under forcing extensions. We give sufficient conditions for a forcing notion to preserve several strengthenings of the Lindel\"of property, such as indestructible…
We prove that the existence of best coapproximation to any element of the normed linear space out of any one dimensional subspace and its coincidence with the best approximation to that element out of that subspace characterizes a real…
We study products of general topological spaces with Menger's covering property, and its refinements based on filters and semifilters. To this end, we extend the projection method from the classic real line topology to the Michael topology.…
Primal characterizations (necessary and sufficient conditions) and slope characterizations of subtransversality, intrinsic transversality and transversality are obtained. The metric nature of intrinsic transversality is established. The…
Some results in C_k-theory are obtained with the use of bornologies. We investigate under which conditions the space of the continuous real functions with the compact-open topology is a productively countably tight space, which yields some…
We give conditions under which a product of topological spaces satisfies some local property. The conditions are necessary and sufficient when the corresponding global property is preserved under finite products. Further examples include…