2024/06/22 by Akhilesh Badra, Hemant Kumar Singh, Badra, Akhilesh +1 · 1 citation
Chemistry · Engineering · Mathematics · #Center (category theory) #Chemistry #Computer network #Computer science #Engineering #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN) #Mathematical analysis #Mathematics #Metric (unit) #Metric space #Operations management #Physics #Primary 54E35 #RADIUS #Secondary 54E99 #Space (punctuation)
paper · pdf · doi:10.48550/arxiv.2406.15772
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce a notion of the center and radius of a subset A of metric space X. In the Euclidean spaces, this notion can be seen as the extension of the center and radius of open/closed balls. The center and radius of a finite product of subsets of metric spaces, and a finite union of subsets of a metric space are also determined. For any subset A of metric space X, there is a natural question to identify the open balls of X with the largest radius that are entirely contained in A. To answer this question, we introduce a notion of quasi-center and quasi-radius of a subset A of metric space X. We prove that the center of the largest open balls contained in A belongs to the quasi-center of A, and its radius is equal to the quasi-radius of A. In particular, for the Euclidean spaces, we see that the center of largest open balls contained in A belongs to the center of A, and its radius is equal to the radius of A.