Translation Results for some Selection Games with Minimal Cusco Maps
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866918143791726592 |
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| author | Caruvana, Christopher Holshouser, Jared |
| author_facet | Caruvana, Christopher Holshouser, Jared |
| contents | We establish relationships between various topological selection games involving the space of minimal cusco maps into the real line and the underlying domain. These connections occur across different topologies, including the topology of pointwise convergence and the topology of uniform convergence on compacta. Full and limited-information strategies are investigated. The primary games we consider are Rothberger-like games, generalized point-open games, strong fan-tightness games, Tkachuk's closed discrete selection game, and Gruenhage's W-games. We also comment on the difficulty of generalizing the given results to other classes of functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_09460 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Translation Results for some Selection Games with Minimal Cusco Maps Caruvana, Christopher Holshouser, Jared General Topology 91A44, 54C60, 54C35, 54D20, 54B20 We establish relationships between various topological selection games involving the space of minimal cusco maps into the real line and the underlying domain. These connections occur across different topologies, including the topology of pointwise convergence and the topology of uniform convergence on compacta. Full and limited-information strategies are investigated. The primary games we consider are Rothberger-like games, generalized point-open games, strong fan-tightness games, Tkachuk's closed discrete selection game, and Gruenhage's W-games. We also comment on the difficulty of generalizing the given results to other classes of functions. |
| title | Translation Results for some Selection Games with Minimal Cusco Maps |
| topic | General Topology 91A44, 54C60, 54C35, 54D20, 54B20 |
| url | https://arxiv.org/abs/2306.09460 |