PreprintarXiv licencearXiv
A solution of the D-space Problem
Abstract
Settling a central problem in set-theoretic topology, and many related problems, we prove that there is, consistently, a regular Lindelöf space of cardinality ℵ1 that is not a D-space. The existence of such a space is independent of ZFC; we establish its equivalence to a weak form of the Continuum Hypothesis. The proof of the main theorem is adjustable to produce consistent examples with a variety of stronger properties.
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BibTeX
@misc{tsaban2026solution,
title = {{A solution of the D-space Problem}},
author = {Boaz Tsaban},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08039},
eprint = {2609.08039},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08039},
}
RIS
TY - UNPB
TI - A solution of the D-space Problem
AU - Boaz Tsaban
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.08039
UR - https://arxiv.org/abs/2609.08039
AB - Settling a central problem in set-theoretic topology, and many related problems, we prove that there is, consistently, a regular Lindelöf space of cardinality ℵ_1 that is not a D-space. The existence of such a space is independent of ZFC; we establish its equivalence to a weak form of the Continuum Hypothesis. The proof of the main theorem is adjustable to produce consistent examples with a variety of stronger properties.
ER -