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Aspects of General Topology Constructive Set Theory
 

Summary: Aspects of General Topology
in
Constructive Set Theory
Peter Aczel 
petera@cs:man:ac:uk
Departments of Mathematics and Computer Science
Manchester University
February 3, 2005
Contents
1 Introduction 2
2 The Galois Adjunction Theorem 5
3 Spaces 8
3.1 Topological superspaces . . . . . . . . . . . . . . . . . . . . . 8
3.2 Constructive and Standard topological spaces . . . . . . . . . 10
4 Locales and formal topologies 13
4.1 Frames and Locales . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2 Set-generated locales . . . . . . . . . . . . . . . . . . . . . . . 14
4.3 Formal topologies . . . . . . . . . . . . . . . . . . . . . . . . . 15
5 Proof of the Galois Adjunction Theorem 18
5.1 Formal points . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

  

Source: Aczel, Peter - Departments of Mathematics & Computer Science, University of Manchester

 

Collections: Mathematics