Point-set games and functions with the hereditary small oscillation property
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929380800856064 |
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| author | Balcerzak, Marek Natkaniec, Tomasz Szuca, Piotr |
| author_facet | Balcerzak, Marek Natkaniec, Tomasz Szuca, Piotr |
| contents | Given a metric space $X$, we consider certain families of functions $f:X\to\mathbb{R}$ having the hereditary oscillation property HSOP and the hereditary continuous restriction property HCRP on large sets. When $X$ is Polish, among them there are families of Baire measurable functions, $\overlineμ$-measurable functions (for a finite nonatomic Borel measure $μ$ on $X$) and Marczewski measurable functions. We obtain their characterizations using a class of equivalent point-set games. In similar aspects, we study cliquish functions, SZ-functions and countably continuous functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15263 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Point-set games and functions with the hereditary small oscillation property Balcerzak, Marek Natkaniec, Tomasz Szuca, Piotr General Topology 91A44 (Primary) 91A05, 54A20, 26A21 (Secondary) Given a metric space $X$, we consider certain families of functions $f:X\to\mathbb{R}$ having the hereditary oscillation property HSOP and the hereditary continuous restriction property HCRP on large sets. When $X$ is Polish, among them there are families of Baire measurable functions, $\overlineμ$-measurable functions (for a finite nonatomic Borel measure $μ$ on $X$) and Marczewski measurable functions. We obtain their characterizations using a class of equivalent point-set games. In similar aspects, we study cliquish functions, SZ-functions and countably continuous functions. |
| title | Point-set games and functions with the hereditary small oscillation property |
| topic | General Topology 91A44 (Primary) 91A05, 54A20, 26A21 (Secondary) |
| url | https://arxiv.org/abs/2405.15263 |