Pointwise tensor products of function spaces

By means of a mixture of linear and nonlinear techniques, the paper treats quasi-Banach function spaces as L∞-modules and studies the basic algebraical constructions and their interactions, placing the emphasis on tensor products. Sample result: if 0→Y→X→Z→0 is an exact sequence of L∞-modules and homomorphisms, where Y and Z are function spaces, and V is another function space, then the tensorized sequence 0→Y⊗V→X⊗V→Z⊗V→0 is exact too.