On the T 1 axiom and other separation properties in constructive point-free and point-set topology

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Annals of Pure and Applied Logic 161 (4):560-569 (2010)
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Abstract

In this note a T1 formal space is a formal space whose points are closed as subspaces. Any regular formal space is T1. We introduce the more general notion of a formal space, and prove that the class of points of a weakly set-presentable formal space is a set in the constructive set theory CZF. The same also holds in constructive type theory. We then formulate separation properties for constructive topological spaces , strengthening separation properties discussed elsewhere. Finally we relate the properties for ct-spaces with corresponding properties of formal spaces

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10.1016/j.apal.2009.03.005

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Citations of this work

On the existence of Stone-Čech compactification.Giovanni Curi - 2010 - Journal of Symbolic Logic 75 (4):1137-1146.
Topological inductive definitions.Giovanni Curi - 2012 - Annals of Pure and Applied Logic 163 (11):1471-1483.
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References found in this work

Aspects of general topology in constructive set theory.Peter Aczel - 2006 - Annals of Pure and Applied Logic 137 (1-3):3-29.
On the collection of points of a formal space.Giovanni Curi - 2006 - Annals of Pure and Applied Logic 137 (1-3):126-146.
Maximal and partial points in formal spaces.Erik Palmgren - 2006 - Annals of Pure and Applied Logic 137 (1-3):291-298.
Exact approximations to Stone–Čech compactification.Giovanni Curi - 2007 - Annals of Pure and Applied Logic 146 (2):103-123.

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