Abstract
In this paper, we investigate ultrametric spaces that satisfy the Unique Midpoint Property (UMP), a condition where every pair of distinct points has a unique midpoint equidistant from both. By analyzing the interaction between the strong triangle inequality of ultrametric spaces and the requirements of the UMP, we derive fundamental constraints on the structure of such spaces. In particular, we prove that in any ultrametric space with the UMP, the distance between any two distinct points equals the distance from each to their unique midpoint. Our main result shows that any ultrametric space satisfying the UMP must be trivial in structure it can only consist of either a single point or exactly three points.
References
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Details
| Primary Language | English |
|---|---|
| Subjects | Applied Mathematics (Other) |
| Journal Section | Research Articles |
| Authors | |
| Early Pub Date | August 20, 2025 |
| Publication Date | |
| Submission Date | February 20, 2025 |
| Acceptance Date | April 18, 2025 |
| Published in Issue | Year 2025Volume: 9 Issue: 2 |
Cite
The works published in Journal of Innovative Science and Engineering (JISE) are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.