  We prove that symplectic homeomorphisms, in the sense of the celebrated
Gromov-Eliashberg Theorem, preserve coisotropic submanifolds and their
characteristic foliations. This result generalizes the Gromov-Eliashberg
Theorem and demonstrates that previous rigidity results (on Lagrangians by
Laudenbach-Sikorav, and on characteristics of hypersurfaces by Opshtein) are
manifestations of a single rigidity phenomenon. To prove the above, we
establish a C^0-dynamical property of coisotropic submanifolds which
generalizes a foundational theorem in C^0-Hamiltonian dynamics: Uniqueness of
generators for continuous analogs of Hamiltonian flows.
