当前位置:文档之家 > The Euclidean Space

The Euclidean Space

FORMALIZEDMATHEMATICS

Vol.2,No.4,September–October1991

Universit´eCatholiquedeLouvain

TheEuclideanSpace

AgataDarmochwa󰀗l

WarsawUniversity

Bia󰀗lystok

Summary.ThegeneraldefinitionofEuclideanSpace.

MMLIdentifier:EUCLID.

Thepapers[14],[6],[9],[8],[12],[1],[5],[10],[3],[13],[4],[15],[16],[7],[11],and[2]providethenotationandterminologyforthispaper.Inthesequelk,ndenotenaturalnumbersandrdenotesarealnumber.Letusconsidern.TheandisdefinedasfunctorRnyieldsanon-emptysetoffinitesequencesof

follows:

(Def.1)Rn=n.

Inthesequelxwilldenoteafinitesequenceofelementsof.Thefunction||fromintoisdefinedasfollows:

(Def.2)foreveryrholds||(r)=|r|.

Letusconsiderx.Thefunctor|x|yieldsafinitesequenceofelement
sof

Letusconsiderx.Thefunctor|x|yieldsafinitesequenceofelementsof

andisdefinedasfollows:

(Def.3)|x|=||·x.

Letusconsidern.Thefunctor󰀊0,...,0󰀋yieldsafinitesequenceofelementsofandisdefinedby:

(Def.4)󰀊0,...,0󰀋=n−→0quaarealnumber.󰀄n󰀆󰀄n󰀆

Letusconsidern.Then󰀊0,...,0󰀋isanelementofRn.

Inthesequelx,x1,x2,ydenoteelementsofRn.Onecanprovethefollowingproposition

(1)xisanelementofn.󰀄n󰀆

601c󰀁1991FondationPhilippeleHodey

ISSN0777–4028

下载Word文档免费下载:

The Euclidean Space下载

(共5页)

TOP相关主题

Summary. The general definition of Euclidean Space.

of Bia?ystok The Euclidean Space Agata Darmochwa? Warsaw University Bia?ystok Summary. The general de?nition of Euclidean Space. MML Identi?er: EUCLID...

On Indefinite Special Lagrangian Submanifolds in Indefinite Complex Euclidean Spaces

On Indefinite Special Lagrangian Submanifolds in Indefinite Complex Euclidean Spaces In this paper, we show that the calibrated method can also be used to...

On the Theory of Surfaces in the Four-dimensional Euclidean Space

On the Theory of Surfaces in the Four-dimensional Euclidean Space On the Theory of Surfaces in the Four-dimensional Euclidean SpaceOn the Theory of ...

Measured Distance Euclidean Space Geometric Distance

Measured Distance Euclidean Space Geometric Distance We propose a new approach to the network distance (roundtrip transmission and propagation delay) ...

Earthquake aftershock networks generated on Euclidean spaces of different fractal geometry

Modelling and Results: In our present work we simulate a network of earthquake aftershocks on Euclidean spaces with di?erent values of the fractal ...

A Covariance Approximation on Euclidean Space for Visual Tracking

A Covariance Approximation on Euclidean Space for Visual Tracking Stefan Kluckner, Thomas Mauthner, and Horst Bischof Institute for Computer Graphics and Vision...

L1calculus on Euclidean space

Ask! Euclidean Space 1.1 Definition: Euclidean 3-Space R3 is the set of all ordered triples of real numbers. Such a triple p=(p1,p2,p3) is ...

On the minimal distance between sets in Euclidean space

of Bia?ystok On the Minimal Distance Between Sets in Euclidean Space1 Andrzej Trybulec University of Bia?ystok Summary. The concept of the minimal ...

Let F be a framework in the Euclidean d-space E

Key Words: In nitesimal exibility, exible polyhedra, octahedra MSC 1994: 53A17 1 Introduction Let F be a framework in the Euclidean d-space E with ...

On the rigidity theorems for Lagrangian translating solitons in pseudo-Euclidean space II

On the rigidity theorems for Lagrangian translating solitons in pseudo-Euclidean space II_教育学/心理学_人文社科_专业资料。International Journal of Mathematics...