On countable star-covering properties

Abstract

We introduce two new notions of topological spaces called a countably starcompact space and a countably absolutely countably compact (= countably acc) space. We clarify the relations between these spaces and other related spaces and investigate topological properties of countably starcompact spaces and countably acc spaces. Some examples showing the limitations of our results are also given.

Keywords

• Countably compact
• Acc
• Starcompact
• Countably starcompact
• Countably acc