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Inductively generated formal topologies

✍ Scribed by Thierry Coquand; Giovanni Sambin; Jan Smith; Silvio Valentini

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
367 KB
Volume
124
Category
Article
ISSN
0168-0072

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✦ Synopsis

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 deÿned.

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