  Every topological space has a Kolmogorov quotient that is obtained by
identifying topologically indistinguishable points, that is, points that are
contained in exactly the same open sets. In this survey, we look at the
relationship between topological spaces and their Kolmogorov quotients. In most
natural examples of spaces, the Kolmogorov quotient is homeomorphic to the
original space. A non-trivial relationship occurs, for example, in the case of
pseudometric spaces, where the Kolmogorov quotient is a metric space. We also
look at the topological indistinguishability relation in the context of
topological groups and uniform spaces.
