Some New Constructions of Ptolemaic andQuasi-Ptolemaic Spaces
DOI:
https://doi.org/10.66147/lnaa.20264494Keywords:
Semimetric space, b-metric space, Ptolemaic space, Quasi-Ptolemaic space, Möbius structure, Absolute cross-ratioAbstract
In this paper, we study the preservation of Ptolemaic and quasi-Ptolemaic properties under various functional transforms and metric constructions. Starting from a given Ptolemaic or quasi-Ptolemaic space, we construct new semimetric and metric structures by introducing specific deformation metrics involving fixed reference points. In particular, we prove that certain weight-based transformations preserve the Ptolemaic condition or yield quasi-Ptolemaic structures with precise control over their defining parameters. Furthermore, we discuss the applications of these metrics in the framework of Möbius structures and b-metric spaces.
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Copyright (c) 2026 Begzod Yuldashev
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