Products of topological spaces and families of filters

We show that, under suitably general formulations, covering properties, accumulation properties and filter convergence are all equivalent notions. This general correspondence is exemplified in the study of products. We prove that a product is Lindelöf if and only if all subproducts by ≤ ω₁ factors are Lindelöf. Parallel results are obtained for final ωₙ-compactness, [ λ, μ ]-compactness, the Menger and the Rothberger properties.