Inductively generated formal topologies
Journal article, 2003

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.

predicative systems

formal topology

inductive definitions


Thierry Coquand

University of Gothenburg

G. Sambin

University of Padua

Jan Smith

Chalmers, Department of Computing Science

S. Valentini

University of Padua

Annals of Pure and Applied Logic

0168-0072 (ISSN)

Vol. 124 1-3 71-106

Subject Categories

Computer and Information Science



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5/9/2018 2