Weak similarities of finite ultrametric and semimetric spaces

Abstract

Weak similarities form a special class of mappings between semimetric spaces. Two semimetric spaces $X$ and $Y$ are weakly similar if there exists a weak similarity $\Phi :X\to Y$. We find a structural characteristic of finite ultrametric spaces for which the isomorphism of its representing trees implies a weak similarity of the spaces. We also find conditions under which the Hasse diagrams of balleans of finite semimetric spaces are isomorphic.

14 pages, 2 figures. arXiv admin note: text overlap with arXiv:2412.17421

Cited by in corpus (2)

• Isomorphism of trees and isometry of ultrametric spaces
• Hereditary properties of finite ultrametric spaces