Sets, complements and boundaries
type: Item
instance of: scholarly article
title: Sets, complements and boundaries
zbMATH Open document ID: 0876.03034
DOI: 10.1016/S0019-3577(97)89131-8
author: Douglas Bridges
author: Fred Richman
author: Yuchuan Wang
published in: Indagationes Mathematicae. New Series
publication date: 1997-03-11T00:00:00Z
review text: A constructive approach to sets, their complements and their boundaries is presented. A constructive theorem on a point of a segment close to the set boundary in a Banach space is used. Brouwerian examples are used to show that the results are best possible. In particular the following questions are addressed: It is possible to compute the distance of any point of a set to its boundary if we can compute the distance of any point of the metric space to the set? If a point is bounded away from the complement of a set, can we show that it is in the set?
Mathematics Subject Classification ID: 03F60
Mathematics Subject Classification ID: 46S30
zbMATH DE Number: 989748
zbMATH Keywords: constructive mathematics
zbMATH Keywords: constructive set theory
zbMATH Keywords: set boundary
zbMATH Keywords: Banach space
zbMATH Keywords: distance
zbMATH Keywords: complement of a set
reviewed by: Pawel Kruszynski
MaRDI profile type: Publication
cites work: Q3679172
cites work: Q3803111
cites work: LOCATEDNESS, CONVEXITY, AND LEBESGUE MEASURABILITY
cites work: Q3754620
cites work: Q4040640
cites work: Q3338243
cites work: Q4001917
cites work: Constructivism in mathematics. An introduction. Volume II
full work available at URL: s0019-3577(97)89131-8
OpenAlex ID: W2009925175
description: scientific article; zbMATH DE number 989748