Some remarks concerning the Mittag-Leffler inverse limit theorem
type: Item
instance of: scholarly article
title: Some remarks concerning the Mittag-Leffler inverse limit theorem
zbMATH Open document ID: 0849.54022
DOI: 10.1007/BF01876355
author: James D. Stein
published in: Periodica Mathematica Hungarica
publication date: 1996-11-11T00:00:00Z
review text: 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.
reviewed by: K. P. Hart
Mathematics Subject Classification ID: 54E52
Mathematics Subject Classification ID: 54E50
zbMATH DE Number: 894312
zbMATH Keywords: inverse sequence of complete metric spaces
zbMATH Keywords: Baire spaces
MaRDI profile type: Publication
cites work: On the Preservation of Baire Category Under Preimages
cites work: Q5516901
cites work: Some observations on local uniform boundedness principles
cites work: Q4277384
full work available at URL: https://doi.org/10.1007/bf01876355
OpenAlex ID: W2918556592
description: scientific article; zbMATH DE number 894312