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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.19745 |
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| _version_ | 1866910720621281280 |
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| author | Michler, Finn Ghosh, Argha |
| author_facet | Michler, Finn Ghosh, Argha |
| contents | We introduce multi-split continuous functions between topological spaces, a weaker form of continuity that generalizes split continuity while being stable under compositions. We will define the associated star multifunction and pre-multi-split multifunctions. Moreover, we will prove that multi-split continuity naturally emerges as the continuity property of selections of finite usco maps, relating their study to set-valued analysis. Finally, we introduce split homeomorphisms and split homeomorphic spaces, showing that for compact, regular Hausdorff spaces, split homeomorphisms characterize deformations with cuts and subsequent re-glues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19745 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Multi-Split Continuity and Split Homeomorphisms Michler, Finn Ghosh, Argha General Topology 54C08, 54C60, 54C65 We introduce multi-split continuous functions between topological spaces, a weaker form of continuity that generalizes split continuity while being stable under compositions. We will define the associated star multifunction and pre-multi-split multifunctions. Moreover, we will prove that multi-split continuity naturally emerges as the continuity property of selections of finite usco maps, relating their study to set-valued analysis. Finally, we introduce split homeomorphisms and split homeomorphic spaces, showing that for compact, regular Hausdorff spaces, split homeomorphisms characterize deformations with cuts and subsequent re-glues. |
| title | On Multi-Split Continuity and Split Homeomorphisms |
| topic | General Topology 54C08, 54C60, 54C65 |
| url | https://arxiv.org/abs/2411.19745 |