可逆过滤器
Reversible filters
摘要：
一个空间是可逆的，如果这个空间到自身上的每一个连续双射都是同胚。本文研究了具有唯一非孤立点的可数空间的可逆性问题。通过Stone对偶，这些空间对应于自然数$βω$的Čech-Stone紧化中的闭子集。由此，出现了以下自然问题：给定可嵌入$βω$中的空间$X$，是否可以以这样的方式嵌入$X$，即相关的邻域过滤器定义了可逆（或不可逆）空间？在某些情况下，我们给出了这个问题的解决方案。特别有趣的是，所需嵌入的图像是否是弱$P$集。
英文摘要：
A space is reversible if every continuous bijection of the space onto itself is a homeomorphism. In this paper we study the question of which countable spaces with a unique non-isolated point are reversible. By Stone duality, these spaces correspond to closed subsets in the Čech-Stone compactification of the natural numbers $βω$. From this, the following natural problem arises: given a space $X$ that is embeddable in $βω$, is it possible to embed $X$ in such a way that the associated filter of neighborhoods defines a reversible (or non-reversible) space? We give the solution to this problem in some cases. It is specially interesting whether the image of the required embedding is a weak $P$-set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
