Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915074838364160 |
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| author | Monteiro, Rodrigo Santos |
| author_facet | Monteiro, Rodrigo Santos |
| contents | Convergence spaces are a generalization of topological spaces. The category of convergence spaces is well-suited for Algebraic Topology, one of the reasons is the existence of exponential objects provided by continuous convergence. In this work, we use a net-theoretic approach to convergence spaces. The goal is to simplify the description of continuous convergence and apply it to problems related to homotopy theory. We present methods to develop the basis of homotopy theory in limit spaces, define the fundamental groupoid, and prove the groupoid version of the Seifert-van Kampen Theorem for limit spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11011 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Monteiro, Rodrigo Santos Algebraic Topology General Topology Convergence spaces are a generalization of topological spaces. The category of convergence spaces is well-suited for Algebraic Topology, one of the reasons is the existence of exponential objects provided by continuous convergence. In this work, we use a net-theoretic approach to convergence spaces. The goal is to simplify the description of continuous convergence and apply it to problems related to homotopy theory. We present methods to develop the basis of homotopy theory in limit spaces, define the fundamental groupoid, and prove the groupoid version of the Seifert-van Kampen Theorem for limit spaces. |
| title | Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces |
| topic | Algebraic Topology General Topology |
| url | https://arxiv.org/abs/2412.11011 |