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On the T1 Axiom and Other Separation Properties in Constructive Point-free and
 

Summary: On the T1 Axiom and Other Separation
Properties in Constructive Point-free and
Point-set Topology
Peter Aczel
Giovanni Curi
First draft: September 25, 2005; this version: December 27,
2008
Abstract
In this note a T1 formal space (T1 set-generated locale) is a for-
mal space whose points are closed as subspaces. Any regular formal
space is T1. We introduce the more general notion of T
1 formal space,
and prove that the class of points of a weakly set-presentable T
1 for-
mal space is a set in the constructive set theory CZF. The same
also holds in constructive type theory. We then formulate separation
properties T
i for constructive topological spaces (ct-spaces), strength-
ening separation properties discussed elsewhere. Finally we relate the
T

  

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

 

Collections: Mathematics