e/Pullback bundle

Information
has gloss	eng: In mathematics, a pullback bundle or induced bundle is a useful construction in the theory of fiber bundles. Given a fiber bundle π : E → B and a continuous map f : B′ → B one can define a "pullback" of E by f as a bundle fE over B′. The fiber of fE over a point x in B′ is just the fiber of E over f(x). Thus f*E is the disjoint union of all these fibers equipped with a suitable topology.
lexicalization	eng: Pull-back bundle
lexicalization	eng: pullback bundle
instance of	e/Fiber bundle

Meaning
Russian
has gloss	rus: Индуцированное расслоение — расслоение f^(\pi)\colon E\to B, индуцированное отображением f\colon B\to B и расслоением \pi\colon E\to B, где E — подпространство прямого произведения B\times E, состоящее из пар (b,e), для которых f(b)=\pi(e), и f^(\pi) \colon (b,e)\mapsto b'.
lexicalization	rus: Индуцированное расслоение
Chinese
has gloss	zho: 数学上，拉回丛（pullback bundle）或导出丛（induced bundle）是纤维丛理论中的常见构造。令 π : E → B为以F为纤维的纤维丛，并令f : B′ → B为任意连续映射。则，f自然地诱导出一个纤维丛f*E over B′，它也以F为纤维。大致来讲，只需要说在点x的纤维是在点f(x)的纤维就可以了；然后用不交并将所有纤维合起来。
lexicalization	zho: 拉回丛

Media
media:img	PullbackBundle-01.png