Some topics related to metrics and norms, including ultrametrics and ultranorms, 2

TL;DR

This paper explores collections of semimetrics and seminorms, focusing on ultrametrics and ultranorms, and investigates their geometric properties related to connectedness and topological dimension 0.

Contribution

It provides new insights into the geometric and topological properties of ultrametrics and ultranorms within the framework of semimetrics and seminorms.

Findings

Analysis of connectedness properties of ultrametrics

Characterization of topological dimension 0 in these spaces

Insights into the structure of ultranorms

Abstract

Here we look at (collections of) semimetrics and seminorms, including their ultrametric versions. In particular, we are concerned with geometric properties related to connectedness and topological dimension 0.