New Pseudodistances Associated with Reparametrization Invariant Seminorms

TL;DR

This paper introduces new pseudodistances for measuring differences between pairs of topological spaces and functions, based on reparametrization invariant seminorms, with an illustrative example.

Contribution

The paper proposes novel pseudodistances linked to reparametrization invariant seminorms for pairs of topological spaces and functions.

Findings

Introduction of new pseudodistances for pairs of spaces and functions

Application of these pseudodistances with an illustrative example

Potential for measuring differences invariant under reparametrizations

Abstract

We consider pairs of a non-empty compact connected and locally connected Hausdorff space and a real-valued continuous function. Our aim is to measure the difference between this kind of the pairs. In this notes we introduce new pseudodistances between pairs associated with reparametrization invariant seminorms. We finish with an example where the use of this lower bound is illustrated.