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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.13220 |
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Table of Contents:
- A space $X$ is od-Menger if it satisfies $\mathsf{U_{fin}}(Δ_X, \mathcal{O}_X)$, where $\mathcal{O}_X,Δ_X$ are the collection of covers of $X$ by respectively open subsets and open dense subsets. We show that under CH, there is a refinement of the usual topology on a subset of the reals which yields a hereditarily Lindelöf, od-Menger, non-Menger, $0$-dimensional, first countable space. We also investigate the properties of spaces which are od-Menger but not Menger.