Separatedness in constructive topology
type: Item
instance of: scholarly article
title: Separatedness in constructive topology
zbMATH Open document ID: 1037.54020
published in: Documenta Mathematica
publication date: 2004-01-19T00:00:00Z
full work available at URL: https://eudml.org/doc/50764
full work available at URL: 17.html
review text: This interesting paper continues the authors' extensive study of the constructive aspects of topological spaces. Classically, Hausdorff topological spaces may be characterized by any one of three (classically equivalent) conditions. These conditions (stated quite imprecisely here) are: (H) Distinct points have disjoint open neighborhoods. (N1) A net may have at most one limit. (N2) If a net converges to a point, then it is eventually bounded away from any other point. The paper determines the constructive relationships between these conditions. The various terms, such as distinct, disjoint, and complement, are given precise definitions, which include several constructively-distinct variations. The main results are that (H) and (N2) are constructively equivalent, and if the inequality relation has a certain extra property, they imply (N1). Brouwerian examples are given to show that these results are the best possible in a constructive framework.
reviewed by: Mark Mandelkern
Mathematics Subject Classification ID: 54D10
Mathematics Subject Classification ID: 03F60
zbMATH DE Number: 2028923
author: Douglas Bridges
author: Luminiţa Viţă
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2028923