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March 6, 2026FilomatOpen Access

Center and radius of a subset of a metric space

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Authors

ABAkhilesh BadraHSHemant Singh

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Overview

Introduces center and radius definitions for subsets in metric spaces, suggesting new geometric insights.

Key Points

  • The aim is to define and explore the concepts of center and radius for subsets of metric spaces, extending traditional ideas from Euclidean spaces.
  • Introduced definitions for center and radius of subsets in metric spaces.
  • Analyzed finite products and unions of subsets.
  • Developed concepts of quasi-center and quasi-radius for subsets.
  • Proved relationships between centers of open balls and quasi-centers.
  • Centers of largest open balls in a subset A are shown to belong to the quasi-center of A.
  • The radius of the largest open balls is equal to the quasi-radius of A.
  • For Euclidean spaces, the center of A aligns with the centers of the largest open balls.

Cite This Study

Badra et al. (2025) studied this question.

synapsesocial.com/papers/69aa701a531e4c4a9ff59945https://doi.org/10.2298/fil2520017b
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