This paper clarifies the topology of the mapping between v- and n-space 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.Comment: 4 pages, 4 figures (1 color
