In [1] several conditions are described which imply the closedness of linear images of convex sets. Here we combine two such theorems into a common generalization. We give a proof of the general theorem which is simpler than the proof obtained by combining the proofs of the two theorems. The paper is almost self-contained as we give transparent proofs of the separation theorems used. Also we present an application of our general closedness theorem in the theory of duality in convex programming. [1] R. T. Rockafellar, Convex analysis, Princeton University Press, Princeton, 1970.

## Citation

Operation Research Report 2005-2, Eötvös Loránd University Budapest, H-1117 Budapest, Pázmány Péter 1/c, Hungary