A note on δ-strongly compact cardinals

In this paper we investigate more characterizations and applications of δ-strongly compact cardinals. We show that, for a cardinal κ the following are equivalent: (1) κ is δ-strongly compact, (2) For every regular λ ≥ κ there is a δ-complete uniform ultrafilter over λ, and (3) Every product space of δ-Lindelöf spaces is κ-Lindelöf. We also prove that in the Cohen forcing extension, the least ω₁-strongly compact cardinal is a precise upper bound on the tightness of the products of two countably tight spaces.