The aim of this paper is to continue the work started in Pavlović (Filomat 30(14):3725–3731, 2016) . We investigate further the properties of the local closure function and the spaces defined by it using common ideals, like ideals of finite sets, countable sets, closed and discrete sets, scattered sets and nowhere dense sets. Also, closure compatibility between the topology and the ideal, idempotency, and cases when the local closure of the whole space X is X or a proper subset of X, are closely investigated. In the case of closure compatibility and idempotency of the local closure function, the topology obtained by the local closure function is completely described.

本文的目的是继续在 Pavlović (Filomat 30(14):3725–3731, 2016) 中开始的工作。我们进一步研究了局部闭包函数的性质及其使用共同理想定义的空间，如有限集、可数集、封闭和离散集、分散集和无处稠密集的理想。此外，拓扑和理想，幂等，当整个空间的局部封闭的情况下关闭之间的兼容性X是X或真子集X，是密切调查。在局部闭包函数具有闭包兼容性和幂等性的情况下，完整描述了局部闭包函数得到的拓扑结构。