  If the assumption that physical space has a trivial topology is dropped, then
the Universe may be described by a multiply connected Friedmann-Lema\^{\i}tre
model on a sub-horizon scale. Specific candidates for the multiply connected
space manifold have already been suggested. How precisely would a significant
detection of multiple topological images of a single object, or a region on the
cosmic microwave background, (due to photons arriving at the observer by
multiple paths which have crossed the Universe in different directions),
constrain the values of the curvature parameters $\Omega_0$ and $\lambda_0$?
  The way that the constraints on $\Omega_0$ and $\lambda_0$ depend on the
redshifts of multiple topological images and on their radial and tangential
separations is presented and calculated. The tangential separations give the
tighter constraints: multiple topological images of known types of
astrophysical objects at redshifts $z \ltapprox 3$ would imply values of
$\Omega_0$ and $\lambda_0$ preciser than $\sim 1%$ and $\sim 10%$ respectively.
Cosmic microwave background `spots' identified with lower redshift objects by
the Planck or MAP satellites would provide similar precision. This method is
purely geometrical: no dynamical assumptions (such as the virial theorem) are
required and the constraints are independent of the Hubble constant, $H_0.$
