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 (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 06 December 2021

SPACES AS COMONOIDS

SPACES AS COMONOIDS

Chapter:
(p.193) 12 SPACES AS COMONOIDS
Source:
From Sets and Types to Topology and Analysis
Author(s):

A. Bucalo

G. Rosolini

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566519.003.0012

The constructive approach to topology has produced a wealth of new insights about spaces, almost reaching the point of making these more elementary than sets. In particular, the point of view taken by the notion of the basic picture as developed in the context of formal topology brings forward the relevance of relations between sets as an elementary constituent for understanding topological spaces. The chapter employs the language and notions of category theory to put the concept of the basic pair under scrutiny. It gives a presentation of topological spaces, which exploits another monoidal structure on the category of complete sup-lattices compared with the one given by Galois connections as in the memoirs by Joyal and Tierney. In this modified context, this chapter characterizes the frames which are topologies.

Keywords:   formal topology, basic picture, relations, topological space, category theory, Joyal, Tierney

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 .