Distance between compact set and point in constructive metric space

Xinyu Shi; Haoyan Zhong; Wei Lyu; Tong Qiu; Zijian Li

doi:10.1117/12.2628180

22 April 2022 Distance between compact set and point in constructive metric space

Xinyu Shi, Haoyan Zhong, Wei Lyu, Tong Qiu, Zijian Li

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 121632Z (2022) https://doi.org/10.1117/12.2628180
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

In metric space, for any fixed point outside the compact set, we can always find a point within the compact set that minimizes the distance between two points. Whether it still has the same property in the constructive metric space is the focus of this paper. Based on the constructive real number and constructive metric space, this paper discusses this property in constructive metric space, and we explore the distance function between a point and a compact set in the constructive metric space. Then we constructed an example of constructive metric space 𝑋 such that no algorithm can always choose one point 𝑐 of compact set 𝐶 𝑖𝑛 𝑋 which is the closest point to a given point 𝑥 ∈ 𝑋. Eventually, the conclusion of constructive metric space is different from that in metric space, which shows the difference between metric space and constructive metric space.

Citation Download Citation

Xinyu Shi, Haoyan Zhong, Wei Lyu, Tong Qiu, and Zijian Li "Distance between compact set and point in constructive metric space", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 121632Z (22 April 2022); https://doi.org/10.1117/12.2628180

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