σ-α-pseudocompact

Definition

A topological space X is called σ-α-pseudocompact if it is σ-C_α-compact in itself (i.e. there is a countable cover {X_n} where each X_n is C_α-compact).

Reference

Angel Tamariz-Mascarua, α-Pseudocompactness in C_p-spaces, Topology Proceedings, Vol.23, Summer 1998, 349-362.