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The identifiability of parameters in a model with known structure and no noise is the problem of accurate determination of the number of parameter space points which are solutions to the identification problem. Using the norm-coerciveness theorem, we demonstrate a result on global identifiability. We introduce the idea of a strong separator of the parameter space, which divides this space into various connected domains; in each of these domains there is one and only one solution to the problem of identification of parameters. To simplify the presentation, notations and examples of linear compartmental models are used here, but the main result (Theorem 3) is valid for all linear systems. Unfortunately, it is not always possible to use this result because the assumptions of this theorem are strong.