upper semicontinuous decomposition

upper semicontinuous decomposition

[′əp·ər ¦sem·i·kən′tin·yə·wəs dē‚käm·pə′zish·ən] (mathematics) A partition of a topological space with the property that for every member D of the partition and for every open set U containing D there is an open set V containing D which is contained in U and is the union of members of the partition.