weakly compact

Definition

A topological space is called weakly compact if every regular open cover has a finite subfamily whose closure covers it.

Reference

S. Balasubramanian, C.Sandhya and P.Aruna Swathi Vyjayanthi, Note on Regularity and ν-compactness, Int. J. Contemp. Math. Sciences, Vol. 5, (2010) no. 16, 777-784