In the mathematical study of metric spaces, one can consider the arclength of paths in the space. If two points are at a given distance from each other, it is natural to expect that one should be able to get from the first point to the second along a path whose arclength is equal to (or very close to) that distance. The distance between two points of a metric space relative to the intrinsic metric is defined as the infimum of the lengths of all paths from the first point to the second. A metric space is a length metric space if the intrinsic metric agrees with the original metric of the space.
| Attributes | Values |
|---|
| rdfs:label
| - Innere Metrik (de)
- Metrica intrinseca (it)
- Intrinsic metric (en)
- Espace de longueur (fr)
- 길이 거리 공간 (ko)
- Внутренняя метрика (ru)
- Внутрішня метрика (uk)
|
| rdfs:comment
| - In der Mathematik misst die innere Metrik oder Längenmetrik die Längen minimaler Verbindungswege zwischen Punkten. (de)
- En mathématiques, un espace de longueur est un espace métrique particulier, qui généralise la notion devariété riemannienne : la distance y est définie par une fonction vérifiant une axiomatique la rendant proche de l'idée concrète de distance.Les espaces de longueur ont été étudiés au début du XXe siècle par (en) et (en) sous le nom d'espaces métriques intrinsèques, et réintroduits plus récemment par Mikhaïl Gromov. (fr)
- 거리 공간 이론에서, 길이 거리 공간(-距離空間, 영어: length metric space)은 두 점 사이의 거리가 두 점을 잇는 곡선들의 길이들의 하한으로 주어지는 거리 공간이다. (ko)
- Внутрішня метрика — метрика простору, що визначається за допомогою функціоналу довжини, як інфімум довжин усіх шляхів (кривих), що з'єднують дану пару точок. (uk)
- Внутренняя метрика — метрика в пространстве, определяемая с помощью функционала длины, как инфимум длин всех путей (кривых), соединяющих данную пару точек. (ru)
- In the mathematical study of metric spaces, one can consider the arclength of paths in the space. If two points are at a given distance from each other, it is natural to expect that one should be able to get from the first point to the second along a path whose arclength is equal to (or very close to) that distance. The distance between two points of a metric space relative to the intrinsic metric is defined as the infimum of the lengths of all paths from the first point to the second. A metric space is a length metric space if the intrinsic metric agrees with the original metric of the space. (en)
- Nello studio matematico degli spazi metrici, si può considerare la lunghezza d'arco dei cammini nello spazio. Se due punti sono a una certa distanza l'uno dall'altro, è naturale aspettarsi che si dovrebbe essere in grado di arrivare da un punto all'altro lungo un cammino la cui lunghezza d'arco sia uguale (o arbitrariamente vicina) alla distanza. (it)
|
| dcterms:subject
| |
| Wikipage page ID
| |
| Wikipage revision ID
| |
| Link from a Wikipage to another Wikipage
| |
| sameAs
| |
| dbp:wikiPageUsesTemplate
| |
| has abstract
| - In der Mathematik misst die innere Metrik oder Längenmetrik die Längen minimaler Verbindungswege zwischen Punkten. (de)
- In the mathematical study of metric spaces, one can consider the arclength of paths in the space. If two points are at a given distance from each other, it is natural to expect that one should be able to get from the first point to the second along a path whose arclength is equal to (or very close to) that distance. The distance between two points of a metric space relative to the intrinsic metric is defined as the infimum of the lengths of all paths from the first point to the second. A metric space is a length metric space if the intrinsic metric agrees with the original metric of the space. If the space has the stronger property that there always exists a path that achieves the infimum of length (a geodesic) then it may be called a geodesic metric space or geodesic space. For instance, the Euclidean plane is a geodesic space, with line segments as its geodesics. The Euclidean plane with the origin removed is not geodesic, but is still a length metric space. (en)
- En mathématiques, un espace de longueur est un espace métrique particulier, qui généralise la notion devariété riemannienne : la distance y est définie par une fonction vérifiant une axiomatique la rendant proche de l'idée concrète de distance.Les espaces de longueur ont été étudiés au début du XXe siècle par (en) et (en) sous le nom d'espaces métriques intrinsèques, et réintroduits plus récemment par Mikhaïl Gromov. (fr)
- 거리 공간 이론에서, 길이 거리 공간(-距離空間, 영어: length metric space)은 두 점 사이의 거리가 두 점을 잇는 곡선들의 길이들의 하한으로 주어지는 거리 공간이다. (ko)
- Nello studio matematico degli spazi metrici, si può considerare la lunghezza d'arco dei cammini nello spazio. Se due punti sono a una certa distanza l'uno dall'altro, è naturale aspettarsi che si dovrebbe essere in grado di arrivare da un punto all'altro lungo un cammino la cui lunghezza d'arco sia uguale (o arbitrariamente vicina) alla distanza. La metrica intrinseca è definita allora come l'estremo inferiore della lunghezza di tutti i cammini che congiungono due punti qualsiasi. Si dimostra innanzitutto che la definizione dà effettivamente luogo a una metrica sullo spazio, e quindi che tale metrica che gode di alcune proprietà peculiari. (it)
- Внутрішня метрика — метрика простору, що визначається за допомогою функціоналу довжини, як інфімум довжин усіх шляхів (кривих), що з'єднують дану пару точок. (uk)
- Внутренняя метрика — метрика в пространстве, определяемая с помощью функционала длины, как инфимум длин всех путей (кривых), соединяющих данную пару точек. (ru)
|
| prov:wasDerivedFrom
| |
| page length (characters) of wiki page
| |
| foaf:isPrimaryTopicOf
| |
| is Link from a Wikipage to another Wikipage
of | |
| is Wikipage redirect
of | |
| is foaf:primaryTopic
of | |
![[RDF Data]](/fct/images/sw-rdf-blue.png)
![[cxml]](/fct/images/cxml_doc.png)
![[csv]](/fct/images/csv_doc.png)
![[text]](/fct/images/ntriples_doc.png)
![[turtle]](/fct/images/n3turtle_doc.png)
![[ld+json]](/fct/images/jsonld_doc.png)
![[rdf+json]](/fct/images/json_doc.png)
![[rdf+xml]](/fct/images/xml_doc.png)
![[atom+xml]](/fct/images/atom_doc.png)
![[html]](/fct/images/html_doc.png)