Presented is a theoretical framework for variables and their control taking approximate behavior ("fuzziness") into account. In our definition of variables the domain of a variable is parameterized by control parameters, the theoretical concepts used are from classical topology. The tools are topological filter bases, or dual, ideal bases, to define neighborhood structures and generalized distances to a set of states or a set of control parameters, measures of approximation, limits in the control and in the state space. Further, we consider homomorphic mappings of bases, control selection for convergent approximations, control structures for state transitions in uniform topological spaces.