Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2605.04851 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
Tabla de Contenidos:
- 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.