Inductively generated formal topologies

Annals of Pure and Applied Logic 124 (1-3):71-106 (2003)
Authors
Jennifer Smith
University of Canterbury
Abstract
Formal topology aims at developing general topology in intuitionistic and predicative mathematics. Many classical results of general topology have been already brought into the realm of constructive mathematics by using formal topology and also new light on basic topological notions was gained with this approach which allows distinction which are not expressible in classical topology. Here we give a systematic exposition of one of the main tools in formal topology: inductive generation. In fact, many formal topologies can be presented in a predicative way by an inductive generation and thus their properties can be proved inductively. We show however that some natural complete Heyting algebra cannot be inductively defined
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DOI 10.1016/s0168-0072(03)00052-6
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References found in this work BETA

Tychonoff's Theorem in the Framework of Formal Topologies.Sara Negri & Silvio Valentini - 1997 - Journal of Symbolic Logic 62 (4):1315-1332.
On the Formal Points of the Formal Topology of the Binary Tree.Silvio Valentini - 2002 - Archive for Mathematical Logic 41 (7):603-618.
An Intuitionistic Proof of Tychonoff's Theorem.Thierry Coquand - 1992 - Journal of Symbolic Logic 57 (1):28-32.

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Citations of this work BETA

Heyting-Valued Interpretations for Constructive Set Theory.Nicola Gambino - 2006 - Annals of Pure and Applied Logic 137 (1):164-188.
On the Collection of Points of a Formal Space.Giovanni Curi - 2006 - Annals of Pure and Applied Logic 137 (1):126-146.
The Problem of the Formalization of Constructive Topology.Silvio Valentini - 2004 - Archive for Mathematical Logic 44 (1):115-129.
Compactness in Locales and in Formal Topology.Steven Vickers - 2006 - Annals of Pure and Applied Logic 137 (1):413-438.

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