Neighborhoods and convergence with respect to a closure operator

Mathematica Slovaca

Josef Šlapal¹ 

关键词: categorical closure operator;    neighborhood;    separation;    compactness;    convergence;   

DOI  :  10.2478/s12175-011-0041-2

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

We study neighborhoods with respect to a categorical closure operator. In particular, we discuss separation and compactness obtained from neighborhoods in a natural way and compare them with the usual closure separation and closure compactness. We also introduce a concept of convergence based on using centered systems of subobjects, which naturally generalizes the classical filter convergence in topological spaces. We investigate behavior of the convergence introduced and show, among others, that it relates to the separation and compactness in natural ways.

【 授权许可】

Unknown