The aim of this paper is twofold. First, to provide a characterization of clopen topologies. We show that a topology is clopen if and only if it is symmetric and Alexandroff. Second, to investigate when some special unitary subrings of a power set define a (clopen) topology.

中文翻译：

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电源组和 cloopen 拓扑的子环

本文的目的是双重的。首先，提供 cloopen 拓扑的表征。我们证明了一个拓扑是封闭的当且仅当它是对称的并且是 Alexandroff。其次，研究幂集的某些特殊酉子环何时定义（闭开）拓扑。