Generalizations of closure operators and neighborhood systems

Abstract

Abstract: By weaking the axioms of closure operators in general topology, the notion of generalized closure operator is investigated, and its relations to general neighborhood systems introduced earlier by the authors are studied. In particular, it is proven that there exists a natural complete lattice isomorphism between generalized closure operators and general neighborhood systems.

Key words: topology, generalized neighborhood system, generalized closure operator, complete lattice isomorphism

摘要： 通过弱化一般拓扑中的闭包算子公理，引入了广义闭包算子的概念，研究了其与稍早引入的广义邻域系的关系。特别的，证明了二者之间存在着自然的完备格同构。

关键词: 拓扑学, 广义邻域系, 广义闭包算子, 完备格同构

ZHAO Fangfang, LI Lingqiang. Generalizations of closure operators and neighborhood systems[J]. Computer Engineering and Applications, 2016, 52(21): 68-71.

赵方方，李令强. 闭包算子与邻域系的广义化[J]. 计算机工程与应用, 2016, 52(21): 68-71.

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Generalizations of closure operators and neighborhood systems

闭包算子与邻域系的广义化

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