Some remarks concerning the Mittag-Leffler inverse limit theorem (Q1915644)

The `Mittag-Leffler theorem' alluded to in the title states that if \(\{X_n, f_n: n\in \mathbb{N}\}\) is an inverse sequence of complete metric spaces such that for all \(n\) the image \(f_n [X_{n+1}]\) is dense in \(X_n\), then the projection \(\pi:\varprojlim X_n\to X_1\) has dense image as well. The author shows that the theorem does not hold if the \(X_n\) are merely Baire spaces but provides a form of the theorem that does hold for Baire spaces.