Abstract: 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 \leq \omega_1 factors are Lindelöf. Parallel results are obtained for final \omega_n-compactness, [ \lambda, \mu ]-compactness, the Menger and the Rothberger properties.
Keywords: filter convergence; ultrafilter; product; subproduct; sequential compactness; sequencewise \mathcal P-compactness; Lindelöf property; final \lambda-compactness; [ \mu, \lambda ]-compactness; Menger property; Rothberger property
DOI: DOI 10.14712/1213-7243.2024.005
AMS Subject Classification: 54A20 54B10 54D20