weakly realcompact

Definition

A topological space X is said to be weakly realcompact if every open ultrafilter U with the ccip has a nonempty adherence.

Remark

• It is also called almost realcompact.

Reference

A. Bella and I. V. Yaschenko, Embeddings into first countable spaces with H-closed like properties, Topology and its Applications 83 (1998) 53-61.