Hausdorff characterizations of first countable T1 spaces via fixed point theorems
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911430212583424 |
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| author | Kamburova, Detelina |
| author_facet | Kamburova, Detelina |
| contents | We introduce two notions of a contractive orbit of a set-valued map defined in a first countable space. The first defines the contraction with respect to the topology of the underlying space while the second defines the contraction with respect to a generalized distance function. We characterize the Hausdorff property of first countable $T_1$ spaces via fixed point theorems for set-valued maps with a contractive orbit satisfying some additional assumptions. As an application, we derive a sufficient condition for a function to attain a strong minimum and generalize Cantor's intersection theorem for a sequence of closed nested sets with diameters converging to 0. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17380 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hausdorff characterizations of first countable T1 spaces via fixed point theorems Kamburova, Detelina Functional Analysis We introduce two notions of a contractive orbit of a set-valued map defined in a first countable space. The first defines the contraction with respect to the topology of the underlying space while the second defines the contraction with respect to a generalized distance function. We characterize the Hausdorff property of first countable $T_1$ spaces via fixed point theorems for set-valued maps with a contractive orbit satisfying some additional assumptions. As an application, we derive a sufficient condition for a function to attain a strong minimum and generalize Cantor's intersection theorem for a sequence of closed nested sets with diameters converging to 0. |
| title | Hausdorff characterizations of first countable T1 spaces via fixed point theorems |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2601.17380 |