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Using a dictionary translating a variety of classical and modern coveringproperties into combinatorial properties of continuous images, we get a simpleway to understand the interrelations between these properties in ZFC and in therealm of the trichotomy axiom for upward closed families of sets of naturalnumbers. While it is now known that the answer to the Hurewicz 1927 problem ispositive, it is shown here that semifilter trichotomy implies a negative answerto a slightly weaker form of this problem.Comment: Small update

Combinatorial images of sets of reals and semifilter trichotomy