  We illustrate a physical situation in which topological symmetry, its
breakdown, space-time uncertainty principle, and background independence may
play an important role in constructing and understanding matrix models. First,
we show that the space-time uncertainty principle of string may be understood
as a manifestation of the breakdown of the topological symmetry in the large
$N$ matrix model. Next, we construct a new type of matrix models which is a
matrix model analog of the topological Chern-Simons and BF theories. It is of
interest that these topological matrix models are not only completely
independent of the background metric but also have nontrivial "p-brane"
solutions as well as commuting classical space-time as the classical solutions.
In this paper, we would like to point out some elementary and unsolved problems
associated to the matrix models, whose resolution would lead to the more
satisfying matrix model in future.
