  We introduce a functor which associates to every measure preserving system
(X,B,\mu,T) a topological system (C_2(\mu),\tilde{T}) defined on the space of
2-fold couplings of \mu, called the topological lens of T. We show that often
the topological lens "magnifies" the basic measure dynamical properties of T in
terms of the corresponding topological properties of \tilde{T}. Some of our
main results are as follows: (i) T is weakly mixing iff \tilde{T} is
topologically transitive (iff it is topologically weakly mixing). (ii) T has
zero entropy iff \tilde{T} has zero topological entropy, and T has positive
entropy iff \tilde{T} has infinite topological entropy. (iii) For T a K-system,
the topological lens is a P-system (i.e. it is topologically transitive and the
set of periodic points is dense; such systems are also called chaotic in the
sense of Devaney).
