Injectivity and Projectivity in Analysis and Topology

TL;DR

This paper provides new elementary topological proofs of injectivity results in analysis, leveraging duality between C*-algebras and compact spaces, and extends these results to include group actions.

Contribution

It introduces simpler, more elementary proofs of injectivity in analysis and extends these results to group actions, avoiding complex algebraic tools.

Findings

New proofs for injectivity in analysis using topological duality

Extension of injectivity results to group actions

Simplification of previous proofs by avoiding advanced algebraic concepts

Abstract

We give new proofs for many injectivity results in analysis that make more careful use of the duality between unital abelian C*-algebras and compact Hausdorff spaces. We then extend many of these results to incorporate group actions. Our approach uses only elementary topological constructions and eliminates the need for results from the theory of Boolean algebras and AW*-algebras that were used in earlier proofs.