A new notion of semicontinuity of vector functions and its properties

摘要

A new notion of semicontinuity of vector functions in terms of metrizable spaces called external semicontinuity (esc) is introduced. We present some of its topological and geometrical properties and establish a characterization via the closedness of its epigraph, coepigraph, level and colevel sets. Then esc regularization is studied. Our contributions can be viewed as generalizations of standard results from the scalar case.