Every Lindelöf scattered subspace of a $Σ$-product of real lines is $σ$-compact
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909466247561216 |
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| author | Avilés, Antonio Krupski, Mikołaj |
| author_facet | Avilés, Antonio Krupski, Mikołaj |
| contents | We prove that every Lindelöf scattered subspace of a $Σ$-product of first-countable spaces is $σ$-compact. In particular, we obtain the result stated in the title. This answers some questions of Tkachuk from [Houston J. Math. 48 (2022), no. 1, 171--181]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10035 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Every Lindelöf scattered subspace of a $Σ$-product of real lines is $σ$-compact Avilés, Antonio Krupski, Mikołaj General Topology 54B10, 54D20, 54D45, 54G12 We prove that every Lindelöf scattered subspace of a $Σ$-product of first-countable spaces is $σ$-compact. In particular, we obtain the result stated in the title. This answers some questions of Tkachuk from [Houston J. Math. 48 (2022), no. 1, 171--181]. |
| title | Every Lindelöf scattered subspace of a $Σ$-product of real lines is $σ$-compact |
| topic | General Topology 54B10, 54D20, 54D45, 54G12 |
| url | https://arxiv.org/abs/2411.10035 |