Comparing notions of presentability in Polish spaces and Polish groups

IF 0.6 2区数学 Q2 LOGIC Annals of Pure and Applied Logic Pub Date : 2025-02-18 DOI:10.1016/j.apal.2025.103564

Sapir Ben-Shahar , Heer Tern Koh

引用次数: 0

Abstract

A recent area of interest in computable topology compares different notions of effective presentability for topological spaces. In this paper, we show that up to isometry, there is a compact connected Polish space that has both left-c.e. and right-c.e. Polish presentations, but has no computable Polish presentation. We also construct a Polish group that has both left-c.e. and right-c.e. Polish group presentations, but lacks a computable Polish presentation, up to topological isomorphism.

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比较波兰空间和波兰群体的外观概念

最近在可计算拓扑中出现了一个有趣的领域，比较了拓扑空间的有效表示性的不同概念。在本文中，我们证明了在等距范围内，存在一个紧连的波兰空间，它同时具有左c.e.。和right-c.e。波兰语表示，但没有可计算的波兰语表示。我们还构造了一个波兰族，它同时具有左-c - e。和right-c.e。波兰群表示，但缺乏可计算波兰表示，直至拓扑同构。

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.

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