On Hausdorff operators in ZF $\mathsf {ZF}$

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2023-07-24 DOI:10.1002/malq.202300004

Kyriakos Keremedis, Eleftherios Tachtsis

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引用次数: 0

Abstract

A Hausdorff space $(X, T)$ is called effectively Hausdorff if there exists a function F—called a Hausdorff operator—such that, for every $x, y \in X$ with $x \neq y$ , $F (x, y) = (U, V)$ , where U and V are disjoint open neighborhoods of x and y, respectively. Among other results, we establish the following in $ZF$ , i.e., in Zermelo–Fraenkel set theory without the Axiom of Choice ( $AC$ ):

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关于ZF$\mathsf｛ZF｝中的Hausdorff算子$

如果存在称为豪斯多夫算子的函数F，则豪斯多夫空间（X，T）$（X，\mathcal｛T｝）$被有效地称为豪斯道夫，使得对于每个X，y∈X$X，y\in X$中X≠y$X\ne y$，F（x，y）=（U，V）$F（x）=（U，V）$，其中U和V分别是x和y的不相交的开邻域。在其他结果中，我们在ZF$\mathsf{ZF}$中，即在没有选择公理的Zermelo–Fraenkel集合论（AC$\mathsf{AC}$）中建立了以下结果：

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.