The separation theorem for quasi-closed sets

The concepts of ``closed set, separation and $n$-cell'' are generalized to ``quasi-closed set, weak separation and locally cohesive space,'' respectively. It is then proved that any quasiclosed set $L$, which weakly separates two closed subsets $A,B$ in a locally cohesive ${T_1}$-space $X$, contains a closed set $K$ which separates $A - K$ and $B - K$ in $X$.