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.