finally α-compact

Definition

α is a variable for a cardinality.
Every open cover has a subcover with cardinality at most α.

Remark

• Such a space is also called [α,∞]-compact?.
• In particular, when α=ω, it is simply called finally compact or Lindelöf.

Reference

Manuel Sanchis, Angel Tamariz-Mascarua, p-pseudocompactness and related topics in topological spaces, Topology and its Applications 98 (1999) 323-343.