  We introduce the notion of functionally compact sets into the theory of
nonlinear generalized functions in the sense of Colombeau. The motivation
behind our construction is to transfer, as far as possible, properties enjoyed
by standard smooth functions on compact sets into the framework of generalized
functions. Based on this concept, we introduce spaces of compactly supported
generalized smooth functions that are close analogues to the test function
spaces of distribution theory. We then develop the topological and functional
analytic foundations of these spaces.
