The Unique Midpoint Property in Ultrametric Spaces
Küçük Resim Yok
Tarih
2025
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Bursa Teknik Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Applied Mathematics (Other), Uygulamalı Matematik (Diğer)
Kaynak
Journal of Innovative Science and Engineering
WoS Q Değeri
Scopus Q Değeri
Cilt
9
Sayı
2
