Borel 1 type mappings and the respective equi-families
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912979767787520 |
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| author | Balcerzak, Marek Holá, Ľubica Karlova, Olena Szuca, Piotr |
| author_facet | Balcerzak, Marek Holá, Ľubica Karlova, Olena Szuca, Piotr |
| contents | We investigate classes of functions from a topological space to a metric space that are related to those of Borel class 1. Following the idea defining an equi-Baire 1 family (due to Lecomte) we define the respective equi-families of functions from the considered classes. We observe that studying of equi-families can be reduced to the exploration of a single orbit map with values in a product space. We consider the closure of equi-families with respect to the topology of pointwise convergence. Finally, we investigate functions $f\colon X\times Y\to Z$, for metric spaces $X,Y,Z$, with sections that are equi-continuous, equi-Baire~1 or have equi-generalized Lebesgue property with respect to measurable sets of class $α$. In particular, we generalize a result of Grande. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_15912 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Borel 1 type mappings and the respective equi-families Balcerzak, Marek Holá, Ľubica Karlova, Olena Szuca, Piotr General Topology 54H05 (Primary), 26A21 (Secondary) We investigate classes of functions from a topological space to a metric space that are related to those of Borel class 1. Following the idea defining an equi-Baire 1 family (due to Lecomte) we define the respective equi-families of functions from the considered classes. We observe that studying of equi-families can be reduced to the exploration of a single orbit map with values in a product space. We consider the closure of equi-families with respect to the topology of pointwise convergence. Finally, we investigate functions $f\colon X\times Y\to Z$, for metric spaces $X,Y,Z$, with sections that are equi-continuous, equi-Baire~1 or have equi-generalized Lebesgue property with respect to measurable sets of class $α$. In particular, we generalize a result of Grande. |
| title | Borel 1 type mappings and the respective equi-families |
| topic | General Topology 54H05 (Primary), 26A21 (Secondary) |
| url | https://arxiv.org/abs/2512.15912 |