*Definition [#dba0e3b5]
A topological space X is said to be weakly realcompact if every open ultrafilter U with the [[ccip]] has a nonempty [[adherence>open filter adherence]].

*Remark [#kd3df3d3]
-It is also called [[almost realcompact]].

*Reference [#rdea8e96]
A. Bella and I. V. Yaschenko, ''Embeddings into first countable spaces with H-closed like properties'', Topology and its Applications 83 (1998) 53-61.