Residual stratification and the Cantor-Bendixson structures of dual algebraic coframes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914564037148672 |
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| author | Gangloff, Silvère Nuñez, Alonso |
| author_facet | Gangloff, Silvère Nuñez, Alonso |
| contents | We introduce a notion of residual derivative for elements of a preordered set, a construction that generalizes both the Frattini subgroup in algebra and the Cantor-Bendixson derivative in T1 topological spaces. For dual algebraic coframes with topologies compatible with order, we establish a partial correspondence between the Cantor-Bendixson structure of the lattice and the residual derivatives of its elements. Within this framework, we provide a complete characterization of the first two Cantor-Bendixson levels in terms of the lattice's residual structure. This provides a unified lens through which to study the Cantor-Bendixson structures of topological spaces across domains ranging from algebra to functional analysis and dynamics, facilitating the transfer of analytic techniques between them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04851 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Residual stratification and the Cantor-Bendixson structures of dual algebraic coframes Gangloff, Silvère Nuñez, Alonso Dynamical Systems We introduce a notion of residual derivative for elements of a preordered set, a construction that generalizes both the Frattini subgroup in algebra and the Cantor-Bendixson derivative in T1 topological spaces. For dual algebraic coframes with topologies compatible with order, we establish a partial correspondence between the Cantor-Bendixson structure of the lattice and the residual derivatives of its elements. Within this framework, we provide a complete characterization of the first two Cantor-Bendixson levels in terms of the lattice's residual structure. This provides a unified lens through which to study the Cantor-Bendixson structures of topological spaces across domains ranging from algebra to functional analysis and dynamics, facilitating the transfer of analytic techniques between them. |
| title | Residual stratification and the Cantor-Bendixson structures of dual algebraic coframes |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2605.04851 |