Claim PUB-fprd-program-textbook--siteauto-chapters-08-inverse-limits-tex-2

Exact statement

Proposition 8.2 (Universal property of the inverse limit). Let $Y$ be a set and suppose maps $f_n:Y\to X_n$ form a compatible cone: $\rho_{n+1,n}\circ f_{n+1}=f_n \qquad\text{for every }n.$ There is a unique map $f:Y\longrightarrow\varprojlim_nX_n$ such that $\pi_n\circ f=f_n$ for every coordinate projection $\pi_n$ . If the spaces are topological and every $f_n$ is continuous, then $f$ is continuous.

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Context

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FPRD program textbook, Proposition 8.2 →

Verification notes

Reviewed on 2026-08-25 for stable extraction, publication anchor, and KaTeX validation. No theorem-level hostile proof audit is asserted.

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Open work

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