Using whales to complete a Boolean algebra
type: Item
instance of: scholarly article
title: Using whales to complete a Boolean algebra
zbMATH Open document ID: 1037.06010
author: Jason Holland
published in: Missouri Journal of Mathematical Sciences
publication date: 2004-01-28T00:00:00Z
review text: Let \(B\) be a Boolean algebra and \(A\) be a subset of \(B\). Then \(A\) is called a whale of \(B\) if (1) \(a\in A,\) \(b\in B\) and \(b \leq a\) imply \(b\in A\); (2) sup\(\{a \mid a\in A\}=1\). The author uses the whales of \(B\) to construct the completion of \(B\). This construction leads immediately to the assertion that any Boolean algebra can be represented as a dense subalgebra of all bands of an Archimedean Riesz space.
Mathematics Subject Classification ID: 06E05
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 1982136
zbMATH Keywords: Boolean algebra
zbMATH Keywords: completion
zbMATH Keywords: Archimedean Riesz space
zbMATH Keywords: whale
zbMATH Keywords: bands
reviewed by: Jiří Rachůnek
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1982136