The Lindelöf number of a power; an introduction to the use of elementary submodels in general topology
type: Item
instance of: scholarly article
title: The Lindelöf number of a power; an introduction to the use of elementary submodels in general topology
zbMATH Open document ID: 0836.54004
DOI: 10.1016/0166-8641(94)90071-X
published in: Topology and its Applications
publication date: 1996-05-08T00:00:00Z
review text: Let \(\text{LIND} (\kappa)\) be the one-point compactification of the discrete space of size \(\kappa \geq \omega\). Theorem. The Lindelöf number of \(\text{(LIND} (\kappa))^\omega = \omega_1\). While this theorem is interesting in itself, the author is more interested in using its proof, as the subtitle indicates, as a way to introduce the reader to the use of elementary submodels in general topology. So first he gives a standard combinatorial proof, which is short, elegant, and nearly impenetrable --- where does its structure come from? Then he carefully motivates an elementary submodel proof, whose virtue is, as he points out, that ``the entity we search for is sitting in front of our noses'' - -- no deep intuitions about combinatorial structures are needed here. He then gives the elementary submodel proof in the standard way it would appear, and finally gives a heuristic for such proofs. Anyone unsure about this important technique, in any area in which set theory has been fruitfully applied, would be well advised to read this article.
reviewed by: Judith Roitman
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 54A25
zbMATH DE Number: 609547
zbMATH Keywords: Lindelöf number
zbMATH Keywords: elementary submodel
author: Stephen Watson
MaRDI profile type: Publication
cites work: Q5585136
cites work: Q3472092
cites work: LOCAL DIMENSION OF NORMAL SPACES
cites work: Q4048202
cites work: A normal hereditarily separable non-Lindelöf space
cites work: Q4064169
cites work: Paracompactness and product spaces
full work available at URL: 0166-8641(94)90071-x
OpenAlex ID: W2001902727
description: scientific article; zbMATH DE number 609547