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The following is an Example 6.7.8 in Spanier AT
If $C^*$ is the relative Alexander presheaf of $(X,A)$ (with some coefficient module $G$), the kernel of $\alpha:C^*\to\hat{C}^*$ is $C^*_0$ (the locally zero functions). To show that $\alpha$ satisfies condition (b) (which is gluing property), let...