Abstract

Let X be a set and f : X → X be a map. We denote by 𝒫(f) the topology defined on X whose closed sets are the subsets A of X with f (A) ⊆ A. A topology on X is said to be a primal topology, if it is a 𝒫(f) for some map f. Our aim here is to characterize when the product of an arbitrary family of topological spaces is a primal space.

中文翻译：

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关于原始空间的乘积

摘要

设X是一个集合，f : X → X是一个映射。我们用 𝒫( f ) 表示在X上定义的拓扑，其闭集是 X 的子集A且f ( A) ⊆ A。如果X上的拓扑是 𝒫 (f )一些地图f。我们的目标是描述任意拓扑空间族的乘积何时是原始空间。