Jump to ContentJump to Main Navigation
From Sets and Types to Topology and AnalysisTowards practicable foundations for constructive mathematics$
Users without a subscription are not able to see the full content.

Laura Crosilla and Peter Schuster

Print publication date: 2005

Print ISBN-13: 9780198566519

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198566519.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 25 September 2018

PREDICATIVE EXPONENTIATION OF LOCALLY COMPACT FORMAL TOPOLOGIES OVER INDUCTIVELY GENERATED TOPOLOGIES

PREDICATIVE EXPONENTIATION OF LOCALLY COMPACT FORMAL TOPOLOGIES OVER INDUCTIVELY GENERATED TOPOLOGIES

Chapter:
(p.202) 13 PREDICATIVE EXPONENTIATION OF LOCALLY COMPACT FORMAL TOPOLOGIES OVER INDUCTIVELY GENERATED TOPOLOGIES
Source:
From Sets and Types to Topology and Analysis
Author(s):

Maria Emilia Maietti

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566519.003.0013

Martin Hyland first classified the exponentiable locales as the locally compact ones. This chapter proves the counterpart of Hyland's result for inductively generated formal topologies. More precisely, by adapting Hyland's proofs to the context of formal topology, it proves that locally compact formal covers are the exponentiable objects in the category of inductively generated formal covers. Then, it deduces the analogous result for inductively generated formal topologies (that is, formal topologies with a unary positivity predicate). This demonstrates once more how impredicative reasoning can be unwound predicatively with great patience, but with the benefit of a quite explicit proof.

Keywords:   exponentiation, locales, formal topology, formal covers, inductively generated formal topologies, Martin Hyland

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .