Continuity properties of hyperlat and reducing subspaces

AbstractWe determine points of continuity, upper semicontinuity, and lower semicontinuity of the following two maps from the space of all linear operators on a finite-dimensional complex vector space V into sets of subspaces of V: Hyperlat, which associates with every operator A the set of subspaces invariant under the commutant of A, and Red, which associates with A the set of reducing subspaces of A