We discuss various generalizations of the class of Lindelöf spaces and study the difference between two of these generalizations, the classes of star-Lindelöf and centeredLindelöf spaces.

Abstract In this paper by using hereditary classes [6], we define the notion of γ -Lindelöf modulo called γℋ-Lindelöf and obtain several properties spaces.

We first provide a modified version of the proof in [3] that the Sorgenfrey line is T1. Here, we prove that it is in fact T2, a stronger result. Next, we prove that all subspaces of R (that is the real line with the usual topology) are Lindelöf. We utilize this result in the proof that the Sorgenfrey line is Lindelöf, which is based on the proof found in [8]. Next, we construct the Sorgenfrey p...

We give easy proofs that a) the Continuum Hypothesis implies that if the product of X with every Lindelöf space is Lindelöf, then X is a D-space, and b) Borel’s Conjecture implies every Rothberger space is Hurewicz.

Arhangel’skii proved that if a first countable Hausdorff space is Lindelöf, then its cardinality is at most 20 . Such a clean upper bound for Lindelöf spaces in the larger class of spaces whose points are Gδ has been more elusive. In this paper we continue the agenda started in [50], of considering the cardinality problem for spaces satisfying stronger versions of the Lindelöf property. Infinit...

We introduce a new reflection principle which we call “Fodor-type Reflection Principle” (FRP). This principle follows from but is strictly weaker than Fleissner’s Axiom R. For instance, FRP does not impose any restriction on the size of the continuum, while Axiom R implies that the continuum has size ≤ א2. We show that FRP implies that every locally separable countably tight topological space X...

If B is a compact space and B \ {pt} is Lindelöf then Bκ \ { − → pt} is star-Linedlöf for every κ. If B \ {pt} is compact then Bκ \ { − → pt} is discretely star-Lindelöf. In particular, this gives new examples of Tychonoff discretely star-Lindelöf spaces with unlimited extent.

I survey problems concerning Lindelöf spaces which have partial settheoretic solutions. Lindelöf spaces, i.e. spaces in which every open cover has a countable subcover, are a familiar class of topological spaces. There is a significant number of (mainly classic) problems concerning Lindelöf spaces which are unsolved, but have partial set-theoretic solutions. For example, consistency is known bu...

Given a map T : X → X on a set X we examine under what conditions there is a separable metrizable or an hereditarily Lindelöf or a Lindelöf topology on X with respect to which T is a continuous map. For separable metrizable and hereditarily Lindelöf, it turns out that there is a such a topology precisely when the cardinality ofX is no greater than the cardinality of the continuum. We go onto pr...