Abstract Let Comp be the category of compact Hausdorff spaces with continuous maps. A cover of a space in Comp is an irreducible preimage; equivalent covers are identified. A covering operator (co) is a function c assigning to each X in Comp a cover X ← c X c X which is minimum among covers Y of X with Y = c Y . The family of all such c is denoted coComp. This is a complete lattice (albeit a proper class), with bottom the identity operator id and top the Gleason (extremally disconnected, projective) cover operator g. There is a substantial literature on g and on various other specific covering operators, and on the lattice coComp. Here, we completely determine the atoms (minimal elements above id) in the lattice coComp, show that any c ≠ id in coComp is above an atom, and show that coComp is not atomic. At the end, we make some remarks about what the present paper does and does not tell us about several other categories related to Comp.

中文翻译：

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紧致豪斯多夫空间中覆盖算符格中的原子

摘要 令 Comp 为具有连续映射的紧致 Hausdorff 空间的范畴。Comp 中一个空格的覆盖是一个不可约的原像；确定了等效的封面。覆盖算子 (co) 是一个函数 c 为 Comp 中的每个 X 分配一个覆盖 X ← c X c X，它是 X 的覆盖 Y 中最小的，其中 Y = c Y 。所有此类 c 的族均表示为 coComp。这是一个完整的格（尽管是一个适当的类），底部是恒等算子 id，顶部是 Gleason（极不连接的、投影的）覆盖算子 g。有大量关于 g 和各种其他特定覆盖算子以及格 coComp 的文献。在这里，我们完全确定了晶格coComp中的原子（id以上的最小元素），证明coComp中任何c≠id都在一个原子之上，证明coComp不是原子的。在最后，