The Non-Existence of Algorithm Deciding Whether a Constructive Compact Topological Space is Simply Connected

This paper discusses the non-existence of an algorithm Q always deciding whether a constructive compact topological space is simply connected or not, that is whether its fundamental group is trivial or not. We construct a program R that generates compact topological spaces, then we use R and Q to get an extension of an unextendible function to get the contradiction and finish the proof.

Authors

Guangzhi Sun (ORCID: https://orcid.org/0000-0003-3190-497X)
Zirui Li (ORCID: https://orcid.org/0000-0001-7056-4264)
Shiguang Shen (ORCID: https://orcid.org/0000-0002-9896-7679)
Zheng Li (ORCID: https://orcid.org/0000-0001-8536-1646)
Jiahao Chen (ORCID: https://orcid.org/0000-0002-1974-6975)

Publication Details

Journal: Science and Technology of Engineering Chemistry and Environmental Protection
Published: 2025-02-26
DOI: https://doi.org/10.61173/zdwe3y80
Primary Topic: Computability, Logic, AI Algorithms
Type: article
Field-Weighted Citation Impact: 0.00

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article

The Non-Existence of Algorithm Deciding Whether a Constructive Compact Topological Space is Simply Connected

Guangzhi Sun, Zirui Li, Shiguang Shen, Zheng Li et al.

Feb 26, 2025

Science and Technology of Engineering Chemistry and Environmental Protection

Computability, Logic, AI Algorithms

article

The Non-Existence of Algorithm Deciding Whether a Constructive Compact Topological Space is Simply Connected

Guangzhi Sun, Zirui Li, Shiguang Shen, Zheng Li, Jiahao Chen

February 26, 2025article en

Abstract

This paper discusses the non-existence of an algorithm Q always deciding whether a constructive compact topological space is simply connected or not, that is whether its fundamental group is trivial or not. We construct a program R that generates compact topological spaces, then we use R and Q to get an extension of an unextendible function to get the contradiction and finish the proof.

Science and Technology of Engineering Chemistry and Environmental ProtectionVol. 1(11)

Openalex Percentile: Top 95%

Computability, Logic, AI Algorithms

DOI Open Access PDF OpenAlex

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