The surjection property and computable type
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917715804946432 |
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| author | Amir, Djamel Eddine Hoyrup, Mathieu |
| author_facet | Amir, Djamel Eddine Hoyrup, Mathieu |
| contents | We provide a detailed study of two properties of spaces and pairs of spaces, the surjection property and the epsilon-surjection property, that were recently introduced to characterize the notion of computable type arising from computability theory. For a class of spaces including the finite simplicial complexes, we develop techniques to prove or disprove these properties using homotopy and homology theories, and give applications of these results. In particular, we answer an open question on the computable type property, showing that it is not preserved by taking products. We also observe that computable type is decidable for finite simplicial complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14542 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The surjection property and computable type Amir, Djamel Eddine Hoyrup, Mathieu General Topology Algebraic Topology Logic 54C20, 55M99, 03D78 F.1.1; F.4.1 We provide a detailed study of two properties of spaces and pairs of spaces, the surjection property and the epsilon-surjection property, that were recently introduced to characterize the notion of computable type arising from computability theory. For a class of spaces including the finite simplicial complexes, we develop techniques to prove or disprove these properties using homotopy and homology theories, and give applications of these results. In particular, we answer an open question on the computable type property, showing that it is not preserved by taking products. We also observe that computable type is decidable for finite simplicial complexes. |
| title | The surjection property and computable type |
| topic | General Topology Algebraic Topology Logic 54C20, 55M99, 03D78 F.1.1; F.4.1 |
| url | https://arxiv.org/abs/2306.14542 |