On (non-Menger) spaces whose closed nowhere dense subsets are Menger
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916579236642816 |
|---|---|
| author | Baillif, Mathieu Spadaro, Santi |
| author_facet | Baillif, Mathieu Spadaro, Santi |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13220 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On (non-Menger) spaces whose closed nowhere dense subsets are Menger Baillif, Mathieu Spadaro, Santi General Topology 54D20 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. |
| title | On (non-Menger) spaces whose closed nowhere dense subsets are Menger |
| topic | General Topology 54D20 |
| url | https://arxiv.org/abs/2501.13220 |