p-pseudocompact

Definition

p is a free ultrafilter on ω, the set of natural numbers.
A space is called p-pseudocompact iff every sequence of nonempty open sets has a p-limit point.

Property

• If a space X is p-pseudocompact for some p, it is pseudocompact.

Remark

• For the definition of p-limit, see p-compact.
• For a subspace Y in X, if every sequence of nonempty open subsets in X which meet Y has a p-limit point, it is called p-bounded in X.

Reference

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