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From Sets and Types to Topology and AnalysisTowards practicable foundations for constructive mathematics$
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Laura Crosilla and Peter Schuster

Print publication date: 2005

Print ISBN-13: 9780198566519

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198566519.001.0001

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SEPARATION PROPERTIES IN CONSTRUCTIVE TOPOLOGY

SEPARATION PROPERTIES IN CONSTRUCTIVE TOPOLOGY

Chapter:
(p.176) 11 SEPARATION PROPERTIES IN CONSTRUCTIVE TOPOLOGY
Source:
From Sets and Types to Topology and Analysis
Author(s):

Peter Aczel

Christopher Fox

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566519.003.0011

This chapter studies separation properties in topology as done on the basis of the formal system CZF. Until the 1970s, there was only a limited focus on the general notion of a topological space in constructive mathematics, with most attention being paid to metric space notions both in intuitionistic analysis and in Bishop-style constructive analysis. But in later years, because of the development of topos theory, the study of sheaf models, and work on point-free topology, including work on formal topology, the notions of general topology in constructive mathematics have received more attention. This chapter presents a fairly systematic survey of the main separation properties that topological spaces can have in constructive mathematics. These are perhaps the first kinds of properties to consider when moving from the study of metric spaces to the study of general topological spaces.

Keywords:   topological space, separation properties, Bishop-style constructive mathematics, formal topology, metric space, constructive set theory

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