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.