C_α-compact

Definition

Let α be a cardinal.
A subset B of a topological space X is called C_α-compact if for every continuous function f from X to R^α (the Cartsian product of the reals), the image of B by f is compact in R^α.

Remark

• If α=ω (a countable cardinal), we say simply C-compact.
• If X is C_α-compact in itself, we say X is α-pseudocompact.

Reference

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