σ-C_α-compact

Definition

Let X be a topological space and Y a subspace.
Y is said to be σ-C_α-compact in X if there exists a countable cover {Y_n} of Y where each Y_n is C_α-compact.
X is said to ba σ-α-pseudocompact if it is σ-C_α-compact in itself.

Reference

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