Inductively generated formal topologies
Artikel i vetenskaplig tidskrift, 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

Författare

Thierry Coquand

Göteborgs universitet

G. Sambin

Università di Padova

Jan Smith

Chalmers, Institutionen för datavetenskap

S. Valentini

Università di Padova

Annals of Pure and Applied Logic

0168-0072 (ISSN)

Vol. 124 71-106

Ämneskategorier

Data- och informationsvetenskap

DOI

10.1016/S0168-0072(03)00052-6