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# Productively Lindelöf Spaces May All Be $D$

Published:2011-08-03
Printed: Mar 2013
• Franklin D. Tall,
Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4
 Format: LaTeX MathJax PDF

## Abstract

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.
 Keywords: productively Lindelöf, $D$-space, projectively $\sigma$-compact, Menger, Hurewicz
 MSC Classifications: 54D20 - Noncompact covering properties (paracompact, Lindelof, etc.) 54B10 - Product spaces 54D55 - Sequential spaces 54A20 - Convergence in general topology (sequences, filters, limits, convergence spaces, etc.) 03F50 - Metamathematics of constructive systems