Descriptive complexity of topological invariants

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2025-05-14 DOI:10.1016/j.apal.2025.103611

Djamel Eddine Amir, Mathieu Hoyrup

引用次数: 0

Abstract

In this article, we investigate the descriptive complexity of topological invariants. Our main goal is to understand the expressive power of low complexity invariants, by investigating which spaces they can distinguish. We study the invariants in the first two levels of the Borel hierarchy. We develop techniques to establish whether two spaces can be separated by invariants in these levels. We show that they are sufficient to separate finite topological graphs. We finally identify the complexity of recognizing the line segment.

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拓扑不变量的描述复杂性

在本文中，我们研究了拓扑不变量的描述复杂性。我们的主要目标是通过研究它们可以区分哪些空间来理解低复杂度不变量的表达能力。我们研究了Borel层次结构的前两层中的不变量。我们开发的技术，以确定是否两个空间可以由不变量在这些水平分开。证明了它们足以分离有限拓扑图。最后指出了线段识别的复杂性。

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

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.