A well-quasi-order for continuous functions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912075179098112 |
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| author | Carroy, Raphaël Pequignot, Yann |
| author_facet | Carroy, Raphaël Pequignot, Yann |
| contents | We prove that continuous reducibility is a well-quasi-order on the class of continuous functions between separable metrizable spaces with analytic zero-dimensional domain. To achieve this, we define scattered functions, which generalize scattered spaces, and describe exhaustively scattered functions between zero-dimensional separable metrizable spaces up to continuous equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13150 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A well-quasi-order for continuous functions Carroy, Raphaël Pequignot, Yann Logic Primary 03E15, 26A21, 54C05, 03D55, Secondary 06A07 We prove that continuous reducibility is a well-quasi-order on the class of continuous functions between separable metrizable spaces with analytic zero-dimensional domain. To achieve this, we define scattered functions, which generalize scattered spaces, and describe exhaustively scattered functions between zero-dimensional separable metrizable spaces up to continuous equivalence. |
| title | A well-quasi-order for continuous functions |
| topic | Logic Primary 03E15, 26A21, 54C05, 03D55, Secondary 06A07 |
| url | https://arxiv.org/abs/2410.13150 |