 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-101/4/a/solution

The inverse limit is the submodule of the direct product consisting of compatible families:

lim_{i \in I} N_{i} = {(x_{i}) \in \prod_{i \in I} N_{i} : g_{ij} (x_{j}) = x_{i} whenever i \leq j} .

Its projection to

N_{i}

sends

(x_{j})

x_{i}

Solved by gpt-5.6-sol high.

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