RETRACTED CHAPTER: Algorithmically Detecting Whether a Compact Set is Connected or Not

Rouzhi Wang (), Wangrui Zheng, Zhitian Song and Daniel Yixuan Shi
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Rouzhi Wang: The Experimental High School Attached to Beijing Normal University
Wangrui Zheng: Hangzhou Foreign Languages School
Zhitian Song: The Experimental High School Attached to Beijing Normal University
Daniel Yixuan Shi: The King’s Academy

A chapter in Proceedings of the 8th International Conference on Financial Innovation and Economic Development (ICFIED 2023), 2023, pp 620-626 from Springer

Abstract: Abstract In this work, we study whether there is a program that always terminates the connectiveness of a given Constructive Metric Compact Set (CMCS), a collection of finite epsilon nets formed by computer generated Cauchy sequences with a convergence regulator. If such decisive program $$\mathrm{Q}$$ Q exists, by applying $$\mathrm{Q}$$ Q to a given CMCS’s $$\mathrm{G}(\mathrm{n})$$ G ( n ) , we determine the terminality of an unextendible $$\mathrm{P}(\mathrm{n})$$ P ( n ) which runs with $$\mathrm{G}(\mathrm{n})$$ G ( n ) simultaneously. The universality of $$\mathrm{Q}$$ Q demands the extendiblity of $$\mathrm{P}(\mathrm{n})$$ P ( n ) , and it leads to contradiction. Thus, we prove that finding a program deciding the connectiveness of all CMCSs, which is of some importance in both topology and constructive mathematics, is impossible.

Keywords: CMCS; decisive program; connectedness; constructive mathematics (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:advbcp:978-94-6463-142-5_68

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DOI: 10.2991/978-94-6463-142-5_68

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