Every finite-dimensional analytic space is $σ$-homogeneous
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913276618604544 |
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| author | Agostini, Claudio Medini, Andrea |
| author_facet | Agostini, Claudio Medini, Andrea |
| contents | All spaces are assumed to be separable and metrizable. Building on work of van Engelen, Harrington, Michalewski and Ostrovsky, we obtain the following results: (1) Every finite-dimensional analytic space is $σ$-homogeneous with analytic witnesses, (2) Every finite-dimensional analytic space is $σ$-homogeneous with pairwise disjoint $\mathbfΔ^1_2$ witnesses. Furthermore, the complexity of the witnesses is optimal in both of the above results. This completes the picture regarding $σ$-homogeneity in the finite-dimensional realm. It is an open problem whether every analytic space is $σ$-homogeneous. We also investigate finite unions of homogeneous spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Every finite-dimensional analytic space is $σ$-homogeneous Agostini, Claudio Medini, Andrea General Topology Logic 54H05, 03E15 All spaces are assumed to be separable and metrizable. Building on work of van Engelen, Harrington, Michalewski and Ostrovsky, we obtain the following results: (1) Every finite-dimensional analytic space is $σ$-homogeneous with analytic witnesses, (2) Every finite-dimensional analytic space is $σ$-homogeneous with pairwise disjoint $\mathbfΔ^1_2$ witnesses. Furthermore, the complexity of the witnesses is optimal in both of the above results. This completes the picture regarding $σ$-homogeneity in the finite-dimensional realm. It is an open problem whether every analytic space is $σ$-homogeneous. We also investigate finite unions of homogeneous spaces. |
| title | Every finite-dimensional analytic space is $σ$-homogeneous |
| topic | General Topology Logic 54H05, 03E15 |
| url | https://arxiv.org/abs/2403.14378 |