Some topics related to metrics and norms, including ultrametrics and ultranorms, 3

TL;DR

This paper explores geometric properties like connectedness and topological dimension 0, focusing on ultrametrics and ultranorms, and their implications for metric space theory.

Contribution

It discusses fundamental properties of ultrametrics and ultranorms, highlighting their unique geometric and topological features.

Findings

Ultrametrics satisfy a strong form of the triangle inequality.

Ultrametrics relate to topological dimension 0 and connectedness.

The paper clarifies the role of ultranorms in metric geometry.

Abstract

Some basic geometric properties related to connectedness and topological dimension 0 are discussed, especially in connection with the ultrametric version of the triangle inequality.