On connected subsets of a convergence space
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918151200964608 |
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| author | Herrejón, Bryan Castro Mynard, Frédéric |
| author_facet | Herrejón, Bryan Castro Mynard, Frédéric |
| contents | Though a convergence space is connected if and only if its topological modification is connected, connected subsets differ for the convergence and for its topological modification. We explore for what subsets connectedness for the convergence or for the topological modification turn out to be equivalent. In particular, we show that the largest set containing a given connected set for which all subsets in between are connected is the adherence of the connected set for the reciprocal modification of the convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10939 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On connected subsets of a convergence space Herrejón, Bryan Castro Mynard, Frédéric General Topology 54A20, 54D05, 54B05, 54B30 Though a convergence space is connected if and only if its topological modification is connected, connected subsets differ for the convergence and for its topological modification. We explore for what subsets connectedness for the convergence or for the topological modification turn out to be equivalent. In particular, we show that the largest set containing a given connected set for which all subsets in between are connected is the adherence of the connected set for the reciprocal modification of the convergence. |
| title | On connected subsets of a convergence space |
| topic | General Topology 54A20, 54D05, 54B05, 54B30 |
| url | https://arxiv.org/abs/2506.10939 |