Degeneracy in density functional theory: topology in the v and n spaces

This paper clarifies the topology of the mapping between the v and n spaces in fermionic systems. Density manifolds corresponding to degeneracies g=1 and g>1 are shown to have the same mathematical measure: Every density near a g-ensemble-v-representable (g-VR) n(r) is also g-VR (except "boundary densities" of lower measure). The role of symmetry and the connection between T=0 and T=0(+) are discussed. A lattice model and the Be series are used as illustrations.