Homotopy similarity of maps

TL;DR

This paper introduces a new hierarchy of equivalences on based homotopy classes of maps between cellular spaces, refining the notion of homotopy similarity.

Contribution

It defines a sequence of increasingly fine equivalences on the based-homotopy set [X,Y] for cellular spaces, expanding the understanding of homotopy relations.

Findings

Establishes a hierarchy of homotopy equivalences

Provides a framework for comparing maps at different levels of similarity

Enhances the classification of maps between cellular spaces

Abstract

Given based cellular spaces X and Y, X compact, we define a sequence of increasingly fine equivalences on the based-homotopy set [X,Y].