Subbase countable compactness

A topological space X is S-countably compact for a subbase S of X if for an y infinite subset A C X there is an S-accumulation point p E X of A, i.e. a ny member of S containing the point p contains infinitely many points of A. A space X is called subbase countably compact (in short: SCC) if there is a subbase S of X such that X is S-countably compact. We show that SCC is a productive property, any discrete space of size at least continuum is SCC, but SCC implies countable compactness for X if the Lindelof-degree of X < s .