The concept of a C-space was introduced in 1978 by D. Addis and J. Gresham in order to provide a new class of spaces in dimension theory. We present an internal characterization for an inverse system $\mathbf{X}$ of compact Hausdorff spaces and maps that shows when its limit will be a C-space. This is precisely when $\mathbf{X}$ is a ``C-system,’’ whose definition will be given in this presentation. We use this characterization to construct a C-system $\mathbf{Y}$ so that its inverse limit is a weakly infinite-dimensional, strongly countable-dimensional, metrizable compactum that is a C-space. Finally we introduce a new notion into topological game theory called a game-theoretic C-system.