  The measurements of CMB anisotropy have opened up a window for probing the
global topology of the universe on length scales comparable to and beyond the
Hubble radius. We have developed a new method for calculating the CMB
anisotropy in models with nontrivial topology and apply it to open universe
models with compact spatial topology. We conduct a Bayesian probability
analysis for a selection of models which confronts the theoretical pixel-pixel
temperature correlation function with the COBE-DMR data. Our results
demonstrate that strong constraints on compactness arise: if the universe is
small compared to the `horizon' size, correlations appear in the maps that are
irreconcilable with the observations.
