Algorithmically Detecting Whether a Compact Set is Connected or Not

DOI

10.2991/978-94-6463-142-5_68How to use a DOI?

Keywords

CMCS; decisive program; connectedness; constructive mathematics

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 Q exists, by applying Q to a given CMCS’s G ( n ) , we determine the terminality of an unextendible P ( n ) which runs with G ( n ) simultaneously. The universality of Q demands the extendiblity of 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.

Copyright

© 2023 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Rouzhi Wang
AU  - Wangrui Zheng
AU  - Zhitian Song
AU  - Daniel Yixuan Shi
PY  - 2023
DA  - 2023/05/15
TI  - Algorithmically Detecting Whether a Compact Set is Connected or Not
BT  - Proceedings of the 8th International Conference on Financial Innovation and Economic Development (ICFIED 2023)
PB  - Atlantis Press
SP  - 620
EP  - 626
SN  - 2352-5428
UR  - https://doi.org/10.2991/978-94-6463-142-5_68
DO  - 10.2991/978-94-6463-142-5_68
ID  - Wang2023
ER  -