Star covering properties. (English) Zbl 0743.54007

van Douwen, Eric K.; Reed, G. M.; Roscoe, A. W.; Tree, I. J.

Topology Appl. 39, No. 1, 71-103 (1991).

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.

Reviewer: B.R.Wenner (Kansas City)

MSC:

54D20	Noncompact covering properties (paracompact, Lindelöf, etc.)
54A35	Consistency and independence results in general topology
54E30	Moore spaces

Keywords:

discrete finite chain condition; star-covering properties; discrete countable chain condition

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