*Definition [#v3c3822a]
Every [[δ-open]] cover has a finite subcover.

*Definition 2 [#sc31a48e]
Let X be a topological space and let B be a cover of X. Then X is δ-compact iff every subset family N of X with the properties:
+for any A in B, we can pick some R in N such that A or the complement of A is contained in R
+if U is the topology generated by B, the U-interiors of members of N cover X
has a finite subfamily which covers X.

*Reference [#t019af90]
:Definition 1| Raja Mohammad Latif, ''Topological Properties of δ-Open Sets'', King Fahd University of Petroleum & Minerals, Department of Mathematical Sciences, Technical Report Series, TR409 (2009)
:Definition 2| D.V.Thampuran, ''Nets and Compactness'', Portugaliae Mathematica Vol.28(1) pp.37-54.