On the origins of Dénes König's infinity lemma
type: Item
instance of: scholarly article
title: On the origins of Dénes König's infinity lemma
zbMATH Open document ID: 0880.01006
DOI: 10.1007/BF00376449
author: Miriam Franchella
published in: Archive for History of Exact Sciences
publication date: 1998-02-10T00:00:00Z
review text: In one of its final versions (1927) the lemma reads: If every point of a connected infinite graph has only finitely many edges going to it, then the graph contains an infinite path. In different guises the lemma appeared repeatedly since D. König's constructivist phase around 1914 when it was used in proofs concerned with the Bernstein theorem of set theory and related subjects. D. König was inspired by work of his father Julius König. The interplay of graph theory and set theory in the work of D. König and the emergence of the lemma are described in detail.
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 03-03
Mathematics Subject Classification ID: 05-03
zbMATH DE Number: 1057317
zbMATH Keywords: graph theory
zbMATH Keywords: set theory
Wikidata QID: Q56139779
reviewed by: Detlef Laugwitz
MaRDI profile type: Publication
cites work: Q4133603
cites work: The life and scientific work of Denes König (1884-1944)
cites work: Q3960633
full work available at URL: https://doi.org/10.1007/bf00376449
OpenAlex ID: W45946431
Recommended article: König's Infinity Lemma and Beth's Tree Theorem
Recommended article: On Kelly's lemma for infinite sets of integers
Recommended article: On the infinitesimal Terracini lemma
Recommended article: An infinitary version of the Graham-Leeb-Rothschild theorem
Recommended article: Q3592924
Recommended article: Infinite-dimensional extension of a theorem of Komlós
Recommended article: A Remark on Deligne's Finiteness Theorem
Recommended article: On a lemma of Jacques-Louis Lions and its relation to other fundamental results
Recommended article: Q3728083
Recommended article: An infinitary extension of Jankov's theorem
description: scientific article; zbMATH DE number 1057317