On the class of NY compact spaces of finitely supported elements and related classes

We prove that a compact space K embeds into a -product of compact metrizable spaces (-product of intervals) if and only if K is (strongly countable-dimensional) hereditarily metalindel\"of and every subspace of K has a nonempty relative open second-countable subset. This provides novel characterizations of -Corson and NY compact spaces. We give an example of a uniform Eberlein compact space that does not embed into a product of compact metric spaces in such a way that the -product is dense in the image. In particular, this answers a question of Kubi\'s and Leiderman. We also show that for a compact space K the property of being NY compact is determined by the topological structure of the space Cₚ (K) of continuous real-valued functions of K equipped with the pointwise convergence topology. This refines a recent result of Zakrzewski.