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The study considers the problem of global adaptive stabilisation for a class of uncertain non-linear systems in which the uncertainty may not be parameterised. With the aid of the partition technique of unity in differential topology, global approximation of a function using neural networks is obtained. The usefulness of the approximation theory is shown in the design of a global adaptive neural network controller. It is proved that the proposed design method is able to ensure boundedness of all the signals in the closed loop, and the state variables converge to zero asymptotically.