Metric and topological homology. Projectivity, injectivity and flatness

TL;DR

This work explores metric and topological adaptations of classical homological properties like projectivity, injectivity, and flatness in Banach modules, providing a unified framework for these non-standard homology theories.

Contribution

It introduces a unified approach to studying metric and topological versions of Banach homology properties, expanding the theoretical understanding of Banach modules.

Findings

Developed a unified framework for metric and topological homology theories.

Extended classical homological concepts to non-standard Banach module contexts.

Provided foundational results for further research in Banach homology.

Abstract

In this book we study metric and topological versions of projectivity injectivity and flatness of Banach modules over Banach algebras. These two non-standard versions of Banach homology theories are studied in parallel under unified approach.