Topological classification of chains of linear mappings

TL;DR

This paper establishes that topological isomorphism between chains of linear mappings implies their linear isomorphism, highlighting a strong equivalence between topological and linear classifications in this context.

Contribution

The paper proves that topological and linear isomorphisms coincide for chains of linear mappings, providing a new understanding of their classification.

Findings

Topological isomorphism implies linear isomorphism for chains of linear mappings

Topological and linear classifications are equivalent in this setting

Simplifies classification by reducing topological problems to linear ones

Abstract

We prove that two chains of linear mappings are topologically isomorphic if and only if they are linearly isomorphic.