  Geometry constrains but does not dictate the topology of the 3--dimensional
space. In a locally spatially homogeneous and isotropic universe, however, the
topology of its spatial section dictates its geometry. We show that, besides
determining the geometry, the knowledge of the spatial topology through the
circles--in--the--sky offers an effective way of setting constraints on the
density parameters associated with dark matter ($\Omega_m$) and dark energy
($\Omega_{\Lambda}$). By assuming the Poincar\'e dodecahedral space as the
circles--in--the--sky detectable topology of the spatial sections of the
Universe, we re-analyze the constraints on the density parametric plane
$\Omega_{m}$--$ \Omega_{\Lambda} $ from the current type Ia supenovae (SNe Ia)
plus X-ray gas mass fraction data, and show that a circles--in--the sky
detection of the dodecahedral space topology give rise to strong and
complementary constraints on the region of the density parameter plane
currently allowed by these observational data sets.
