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arXiv · 2609.08039

A solution of the D-space Problem

Boaz Tsaban
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Abstract

We prove that there is, consistently, a regular Lindel\"of space of cardinality $\aleph_1$ that is not a D-space. This settles a central problem in set-theoretic topology, and many related problems. The existence of such a space is independent of ZFC\@. The question whether, consistently, every regular hereditarily Lindel\"of space is a D-space remains open.

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Boaz Tsaban. 2026-09-07. A solution of the D-space Problem. https://arxiv.org/abs/2609.08039

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