Complex projective space has many applications in both mathematics and quantum physics. In algebraic geometry, complex projective space is the home of projective varieties, a well-behaved class of algebraic varieties. In topology, the complex projective space plays an important role as a classifying space for complex line bundles: families of complex lines parametrized by another space. In this context, the infinite union of projective spaces (direct limit), denoted CP∞, is the classifying space K(Z,2). In quantum physics, the wave function associated to a pure state of a quantum mechanical system is a probability amplitude, meaning that it has unit norm, and has an inessential overall phase: that is, the wave function of a pure state is naturally a point in the projective Hilbert space of the state space.