This paper addresses the problem of feedback invariance in geometric control theory by overviewing a framework that is inherently feedback-invariant. Crucial to the coherence of the method are suitable topologies on spaces of vector fields. The formulation also makes reference to the theory of presheaves and sheaves. While the work is addressed squarely at a fundamental problem of control theory, the technical background for the methods expounded upon are sometimes very complex. For this reason, the intent of the paper is to be expository, rather than technical.

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