Productively LindelÃ¶f Spaces May All Be $D$ We give easy proofs that (a) the Continuum Hypothesis implies that if the product of $X$ with every LindelÃ¶f space is LindelÃ¶f, then $X$ is a $D$-space, and (b) Borel's Conjecture implies every Rothberger space is Hurewicz. Keywords:productively LindelÃ¶f, $D$-space, projectively $\sigma$-compact, Menger, HurewiczCategories:54D20, 54B10, 54D55, 54A20, 03F50