On minimal collections of sequences for testing continuity
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913115603468288 |
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| author | Lim, Gyuhyun |
| author_facet | Lim, Gyuhyun |
| contents | We study test sets: subfamilies of sequences converging to a point P that still suffice to detect every discontinuity of real-valued functions at P. Ordered by inclusion, these test sets form a poset. Under natural hypotheses at P, we prove that this poset has a minimal element. We also analyze its maximal chains, showing that some have a least element, while others do not. Finally, on the sequential fan we give a concrete realization in which the minimal test set produced by our construction has strictly smaller cardinality than the full family of convergent sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11397 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On minimal collections of sequences for testing continuity Lim, Gyuhyun Combinatorics General Topology Logic 54A20, 54C30 We study test sets: subfamilies of sequences converging to a point P that still suffice to detect every discontinuity of real-valued functions at P. Ordered by inclusion, these test sets form a poset. Under natural hypotheses at P, we prove that this poset has a minimal element. We also analyze its maximal chains, showing that some have a least element, while others do not. Finally, on the sequential fan we give a concrete realization in which the minimal test set produced by our construction has strictly smaller cardinality than the full family of convergent sequences. |
| title | On minimal collections of sequences for testing continuity |
| topic | Combinatorics General Topology Logic 54A20, 54C30 |
| url | https://arxiv.org/abs/2605.11397 |