Certain observations on selection principles related to bornological covers using ideals
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arXiv
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| Formato: | Preprint |
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2024
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| author | Chandra, D. Das, P. Das, S. |
| author_facet | Chandra, D. Das, P. Das, S. |
| contents | We study selection principles related to bornological covers using the notion of ideals. We consider ideals $\mathcal I$ and $\mathcal J$ on $ω$ and standard ideal orderings $KB, K$. Relations between cardinality of a base of a bornology with certain selection principles related to bornological covers are established using cardinal invariants such as modified pseudointersection number, the unbounding number and slaloms numbers. When $\mathcal I \leq_\square \mathcal J$ for ideals $\mathcal I, \mathcal J$ and $\square\in \{1\text{-}1,KB,K\}$, implications among various selection principles related to bornological covers are established. Under the assumption that ideal $\mathcal I$ has a pseudounion we show equivalences among certain selection principles related to bornological covers. Finally, the $\mathcal I\text{-}\mathfrak B^s$-Hurewicz property of $X$ is investigated. We prove that $\mathcal I\text{-}\mathfrak B^s$-Hurewicz property of $X$ coincides with the $\mathfrak B^s$-Hurewicz property of $X$ if $\mathcal I$ has a pseudounion. Implications or equivalences among selection principles, games and $\mathcal I\text{-}\mathfrak B^s$-Hurewicz property which are obtained from our investigations are described in diagrams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04276 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Certain observations on selection principles related to bornological covers using ideals Chandra, D. Das, P. Das, S. General Topology 54D20, 54C35, 54A25 We study selection principles related to bornological covers using the notion of ideals. We consider ideals $\mathcal I$ and $\mathcal J$ on $ω$ and standard ideal orderings $KB, K$. Relations between cardinality of a base of a bornology with certain selection principles related to bornological covers are established using cardinal invariants such as modified pseudointersection number, the unbounding number and slaloms numbers. When $\mathcal I \leq_\square \mathcal J$ for ideals $\mathcal I, \mathcal J$ and $\square\in \{1\text{-}1,KB,K\}$, implications among various selection principles related to bornological covers are established. Under the assumption that ideal $\mathcal I$ has a pseudounion we show equivalences among certain selection principles related to bornological covers. Finally, the $\mathcal I\text{-}\mathfrak B^s$-Hurewicz property of $X$ is investigated. We prove that $\mathcal I\text{-}\mathfrak B^s$-Hurewicz property of $X$ coincides with the $\mathfrak B^s$-Hurewicz property of $X$ if $\mathcal I$ has a pseudounion. Implications or equivalences among selection principles, games and $\mathcal I\text{-}\mathfrak B^s$-Hurewicz property which are obtained from our investigations are described in diagrams. |
| title | Certain observations on selection principles related to bornological covers using ideals |
| topic | General Topology 54D20, 54C35, 54A25 |
| url | https://arxiv.org/abs/2403.04276 |