Discrete subspaces of countably tight compacta

Our main result is that the following cardinal arithmetic assumption, which is a slight weakening of GCH, “ 2 κ is a finite successor of κ for every cardinal κ ”, implies that in any countably tight compactum X there is a discrete subspace D with | D ¯ | = | X | . This yields a (consistent) confirmation of Alan Dow’s Conjecture 2 from [A. Dow, Closures of discrete sets in compact spaces, Studia Math. Sci. Hung. 42 (2005) 227–234].