发表机构
Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文综述特殊 $T_1$-空间及其不动点定理，介绍 Kupka 的弱拓扑收缩概念，并讨论 $T_1$ 公理保证不动点唯一性及外围/局部 Hausdorff 空间。
AI 中文摘要
在这篇综述中，我们回顾了某些类型的特殊 $T_{1}$ 空间及其相关的不动点定理。Kupka 引入了弱拓扑收缩的概念，它自然地推广了定义在度量空间上的 Lipschitz 收缩。具体而言，Kupka 在任意 $T_{0}$ 空间的乘积中，为具有闭图的弱拓扑收缩建立了一个不动点定理。此外，$T_{1}$ 分离公理被证明能保证此类不动点的唯一性。最后，我们在这些不动点结果的背景下讨论了外围 Hausdorff 空间和局部 Hausdorff 空间。
英文摘要
In this survey, we review certain types of special \(T_{1}\) spaces and their associated fixed-point theorems. Kupka introduced the notion of a feeble topological contraction, which naturally generalizes Lipschitz contractions defined on metric spaces. Specifically, Kupka established a fixed-point theorem for feeble topological contractions possessing a closed graph within the product of arbitrary \(T_{0}\) spaces. Furthermore, the \(T_{1}\) separation axiom is shown to guaranty the uniqueness of such fixed points. Finally, we discuss peripheral Hausdorff and locally Hausdorff spaces within the context of these fixed-point results.
