Smooth spaces versus continuous spaces in models for synthetic differential geometry

Ieke Moerdijk; Gonzalo E. Reyes

doi:10.1016/0022-4049(84)90049-5

Smooth spaces versus continuous spaces in models for synthetic differential geometry

Ieke Moerdijk^*, Gonzalo E. Reyes

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

In topos models for synthetic differential geometry we study connections between smooth spaces (which interpret synthetic calculus) and continuous spaces (which interpret intuitionistic analysis). Our main tools are adjoint retractions of toposes and the standard map from the smooth reals to the continuous reals.

Original language	English
Pages (from-to)	143-176
Number of pages	34
Journal	Journal of Pure and Applied Algebra
Volume	32
Issue number	2
DOIs	https://doi.org/10.1016/0022-4049(84)90049-5
Publication status	Published - May 1984

Keywords

Grothendieck topos
ideals of smooth functions
intuitionistic analysis
locale
Synthetic differential geometry

Access to Document

10.1016/0022-4049(84)90049-5

Cite this

@article{b6ab990be59b4803aa4d64d762705c55,

title = "Smooth spaces versus continuous spaces in models for synthetic differential geometry",

abstract = "In topos models for synthetic differential geometry we study connections between smooth spaces (which interpret synthetic calculus) and continuous spaces (which interpret intuitionistic analysis). Our main tools are adjoint retractions of toposes and the standard map from the smooth reals to the continuous reals.",

keywords = "Grothendieck topos, ideals of smooth functions, intuitionistic analysis, locale, Synthetic differential geometry",

author = "Ieke Moerdijk and Reyes, {Gonzalo E.}",

year = "1984",

month = may,

doi = "10.1016/0022-4049(84)90049-5",

language = "English",

volume = "32",

pages = "143--176",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

publisher = "Elsevier BV",

number = "2",

}

TY - JOUR

T1 - Smooth spaces versus continuous spaces in models for synthetic differential geometry

AU - Moerdijk, Ieke

AU - Reyes, Gonzalo E.

PY - 1984/5

Y1 - 1984/5

N2 - In topos models for synthetic differential geometry we study connections between smooth spaces (which interpret synthetic calculus) and continuous spaces (which interpret intuitionistic analysis). Our main tools are adjoint retractions of toposes and the standard map from the smooth reals to the continuous reals.

AB - In topos models for synthetic differential geometry we study connections between smooth spaces (which interpret synthetic calculus) and continuous spaces (which interpret intuitionistic analysis). Our main tools are adjoint retractions of toposes and the standard map from the smooth reals to the continuous reals.

KW - Grothendieck topos

KW - ideals of smooth functions

KW - intuitionistic analysis

KW - locale

KW - Synthetic differential geometry

UR - http://www.scopus.com/inward/record.url?scp=48749140388&partnerID=8YFLogxK

U2 - 10.1016/0022-4049(84)90049-5

DO - 10.1016/0022-4049(84)90049-5

M3 - Article

AN - SCOPUS:48749140388

SN - 0022-4049

VL - 32

SP - 143

EP - 176

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 2

ER -

Smooth spaces versus continuous spaces in models for synthetic differential geometry

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this