Productively Lindelof spaces may all be D

TL;DR

This paper demonstrates how certain set-theoretic hypotheses imply that specific topological properties of spaces lead to D-spaces and Hurewicz spaces, linking set theory with topology.

Contribution

It provides simple proofs connecting the Continuum Hypothesis and Borel's Conjecture to properties of Lindelof, Rothberger, and Hurewicz spaces.

Findings

CH implies product of X with Lindelof spaces being Lindelof implies X is D

Borel's Conjecture implies Rothberger spaces are Hurewicz

Simplified proofs connecting set theory and topological properties

Abstract

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