pseudo-(α,β)-compact

Definition

Let X be a topological space and let α and β be cardinal numbers.
A family of subsets of X is called locally < β (in X) if for every point x of X there is a neighborhood V of x such that .
The space X is called pseudo-(α,β)-compact if no set of nonempty open subsets of X indexed by α is locally < β.

Remark

• See pseudocompact.

Reference

W. W. Comfort, Products of spaces with properties of pseudo-compactness type, Topology Proc. Vol.4 (1979) pp.51-65.