Star covering properties (Q1814165)

The authors provide a hierarchy of star-covering properties which fit between countable compactness and pseudocompactness: \(n\)-starcompact, strongly \(n\)-starcompact, and a newly defined property, \(\omega\)- starcompact. Lindelöf analogues are also discussed (\(n\)-star- Lindelöf, strongly \(n\)-star-Lindelöf, and a new \(\omega\)-star- Lindelöf), which rank between Lindelöf and the discrete countable chain condition. The implications of these star-covering properties are also examined in the presence of regularity, and further, for Moore spaces. The authors give a helpful collection of counterexamples to differentiate among the various properties.