Affiliation:
1. 1 Eötvös Loránd Tudományegyetem Analízis Tanszék Pázmány Péter sétány 1/c H-1117 Budapest Hungary
2. 2 Hungarian Academy of Sciences Alfréd Rényi Institute of Mathematics HU–1364 Budapest
3. 3 Magyar Tudományos Akadémia Rényi Alfréd Matematikai Kutatóintézet Postafiók 127 H-1364 Budapest Hungary
Abstract
A topological space X is S -countably compact for a subbase S of X if for any infinite subset A X there is an S -accumulation point p 2 X of A, i.e. any member of S containing the point p contains infinitely many points of A. AspaceXis 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 Lindel¨ of-degree of X is SCC, but SCC implies countable compactness for X if the Lindel¨ of-degree of X