hemicontinuous

Adjective

 * 1)  Having the property that if a sequence of points in the domain of a function converges to a point L, then either the sequence of sets that are the images of those points contains a sequence that converges to a point that is in the image of L, or, alternatively, for every element in the image of L,  you can find a sub-sequence in the domain whose image contains a convergent sequence to that element.

Related terms

 * hemicontinuity