Algorithmically detecting whether a compact set is connected or not

Rouzhi Wang; Wangrui Zheng; Zhitian Song; Daniell Yixuan Shi

doi:10.1117/12.2685986

28 July 2023 Algorithmically detecting whether a compact set is connected or not

Rouzhi Wang, Wangrui Zheng, Zhitian Song, Daniell Yixuan Shi

Proceedings Volume 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023); 1275652 (2023) https://doi.org/10.1117/12.2685986
Event: 2023 3rd International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2023), 2023, Tangshan, China

Abstract

In this work, we study whether there is a program always terminating 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.

Citation Download Citation

Rouzhi Wang, Wangrui Zheng, Zhitian Song, and Daniell Yixuan Shi "Algorithmically detecting whether a compact set is connected or not", Proc. SPIE 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023), 1275652 (28 July 2023); https://doi.org/10.1117/12.2685986

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