The surjection property and computable type

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-07-15 DOI:10.1016/j.topol.2024.109020

Djamel Eddine Amir, Mathieu Hoyrup

引用次数: 0

Abstract

We provide a detailed study of two properties of spaces and pairs of spaces, the surjection property and the ϵ-surjection property, that were recently introduced to characterize the notion of computable type arising from computability theory. For a class of spaces including the finite simplicial complexes, we develop techniques to prove or disprove these properties using homotopy and homology theories, and give applications of these results. In particular, we answer an open question on the computable type property, showing that it is not preserved by taking products. We also observe that computable type is decidable for finite simplicial complexes.

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投影性质和可计算类型

我们详细研究了空间和空间对的两个性质，即投射性质和-投射性质，这两个性质是最近引入的，用来描述可计算性理论中的可计算性类型概念。对于包括有限单纯复数在内的一类空间，我们开发了使用同调和同调理论证明或反证这些性质的技术，并给出了这些结果的应用。特别是，我们回答了一个关于可计算类型性质的公开问题，证明了取积并不能保留这一性质。我们还观察到，可计算类型对于有限简单复数是可解的。

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

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.