Volume 29 • Number 1 • 2006   • Relatively Absolutely Countably Compact Spaces Yan-Kui Song Abstract. A subspace Y of a space X is absolutely countably compact(=acc) (strongly absolutely countably compact(=strongly acc)) in X if for every open cover U of X and every dense subspace D⊂X (respectively, D⊂Y) there exists a finite subset F⊂D such that Y⊂St(F,U), where St(F,U)=∪{U∈U:U∩F&ne∅}. In this paper, we investigate the relationships between these spaces and other starcompact spaces by giving some examples, and also study topological properties of relatively absolutely countably compact spaces. 2000 Mathematics Subject Classification: 54A45, 54D20. Full text: PDF