Convergence in [Formula: see text] -quasicontinuous posets

In this paper, we present one way to generalize [Formula: see text] -convergence and [Formula: see text] -convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of [Formula: see text] -continuity and [Formula: see text] -q...

Descripción completa

Detalles Bibliográficos
Autores principales: Ruan, Xiao-jun, Xu, Xiao-quan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4771692/
https://www.ncbi.nlm.nih.gov/pubmed/27026912
http://dx.doi.org/10.1186/s40064-016-1873-6
Descripción
Sumario:In this paper, we present one way to generalize [Formula: see text] -convergence and [Formula: see text] -convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of [Formula: see text] -continuity and [Formula: see text] -quasicontinuity of posets are given. The main results are: (1) a poset P is [Formula: see text] -continuous if and only if the [Formula: see text] -convergence in P is topological; (2) P is [Formula: see text] -quasicontinuous if and only if the [Formula: see text] -convergence in P is topological.

Ejemplares similares