Injectivity and projectivity in analysis and topology

We give new proofs of many injectivity results in analysis that make more careful use of the duality between abelian C*-algebras and topological spaces. We then extend many of these ideas to incorporate the case of a group action. This approach gives new insight into Hamana’s theory of G-injective operator spaces and G-injective envelopes. Our new proofs of these classic results, use only topological methods and eliminate the need for results from the theory of Boolean algebras and AW*-algebras.