English Dictionary

fiber bundle

名詞

アメリカ英語

(American spelling, topology, category theory) A topological space E with a base space B and a fiber space F such that any point x ∈ B has a neighborhood N that is homeomorphic to the product space B × F (that is, the space is locally the product space B × F, although its global structure can be quite different).

日本語の意味

局所的に積空間となる位相空間の構造をもつ対象。具体的には、全体空間E、基底空間B、および繊維Fという3つの位相空間があり、任意の点x ∈ Bの近傍がBとFの直積空間と同相になるが、全体としてはその直積構造を持たない可能性がある。

A fiber bundle is a topological space E with a base space B and a typical fiber F such that every point x ∈ B has a neighborhood U for which the preimage of U in E is homeomorphic to U × F.

ファイバー束とは、全空間Eと基底空間Bおよび典型的繊維Fからなる位相空間で、任意の点x∈BにはEのその点に対応する部分が近傍U×Fと同相になるような近傍Uが存在する。

意味（1）

(American spelling, topology, category theory) A topological space E with a base space B and a fiber space F such that any point x ∈ B has a neighborhood N that is homeomorphic to the product space B × F (that is, the space is locally the product space B × F, although its global structure can be quite different).

A Möbius strip is a fiber bundle which looks locally (i.e., over a connected proper subset of its base space) like the corresponding part of a cylinder S¹⨯0,1 (a Möbius strip and a cylinder have isomorphic base spaces). A Klein bottle is a fiber bundle which looks locally like the corresponding part of a torus S¹⨯S¹ (again they could be thought of as sharing the same base space S¹; cutting out even a single point of that base space makes the cut Klein bottle isomorphic to the cut torus).

fiber bundles （ plural ）