Translation Results for Some Star-Selection Games
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916173646397440 |
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| author | Caruvana, Christopher Holshouser, Jared |
| author_facet | Caruvana, Christopher Holshouser, Jared |
| contents | We continue to explore the ways in which high-level topological connections arise from connections between fundamental features of the spaces, in this case focusing on star-selection principles in Pixley-Roy hyperspaces and uniform spaces. First, we find a way to write star-selection principles as ordinary selection principles, allowing us to apply our translation theorems to star-selection games. For Pixley-Roy hyperspaces, we are able to extend work of M. Sakai and connect the star-Menger/Rothberger games on the hyperspace to the $ω$-Menger/Rothberger games on the ground space. Along the way, we uncover connections between cardinal invariants. For uniform spaces, we show that the star-Menger/Rothberger game played with uniform covers is equivalent to the Menger/Rothberger game played with uniform covers, reinforcing an observation of Lj. Kočinac. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_00329 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Translation Results for Some Star-Selection Games Caruvana, Christopher Holshouser, Jared General Topology 991A44, 54D20, 54B20 We continue to explore the ways in which high-level topological connections arise from connections between fundamental features of the spaces, in this case focusing on star-selection principles in Pixley-Roy hyperspaces and uniform spaces. First, we find a way to write star-selection principles as ordinary selection principles, allowing us to apply our translation theorems to star-selection games. For Pixley-Roy hyperspaces, we are able to extend work of M. Sakai and connect the star-Menger/Rothberger games on the hyperspace to the $ω$-Menger/Rothberger games on the ground space. Along the way, we uncover connections between cardinal invariants. For uniform spaces, we show that the star-Menger/Rothberger game played with uniform covers is equivalent to the Menger/Rothberger game played with uniform covers, reinforcing an observation of Lj. Kočinac. |
| title | Translation Results for Some Star-Selection Games |
| topic | General Topology 991A44, 54D20, 54B20 |
| url | https://arxiv.org/abs/2210.00329 |