In mathematics, the notion of the continuity of functions is not immediately extensible to multivalued mappings or correspondences between two sets A and B. The dual concepts of upper hemicontinuity and lower hemicontinuity facilitate such an extension. A correspondence that has both properties is said to be continuous in an analogy to the property of the same name for functions. In mathematics, the notion of the continuity of functions is not immediately extensible to multivalued mappings or correspondences between two sets A and B. The dual concepts of upper hemicontinuity and lower hemicontinuity facilitate such an extension. A correspondence that has both properties is said to be continuous in an analogy to the property of the same name for functions.