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单词 Covering space
释义

Covering space

原声例句
PBS访谈商业系列

I got into covering space because it's one of the few events that binds us all together in an uplifting way.

我报道了这些太空计划，因为它是少数几个可以以这种令人振奋的方式，把我们联系在一起的事件之一。

CNBC全球经济分析

Having been covering this space for I think four years now, it’s definitely been a learning experience.

我认为已经涵盖这个领域四年了，这绝对是一次学习经历。

NPR音讯 2021年7月合集

That's Brendan Byrne, a reporter covering space at member station WMFE in Florida and also host of the podcast " Are We There Yet? " Brendan, thanks a lot.

以上是布伦丹·伯恩带来的报道，他是佛罗里达州WMFE成员站的太空记者，也是播客节目《我们到了吗？》的主持人。布伦丹，非常感谢。

中文百科

覆叠空间

A covering map satisfies the local triviality condition. Intuitively, such maps locally project a
Gimbal lock occurs because any map T3 → RP3 is not a covering map. In particular, the relevant map carries any element of T3, that is, an ordered triple (a,b,c) of angles (real numbers mod 2π), to the composition of the three coordinate axis rotations Rx(a)∘Ry(b)∘Rz(c) by those angles, respectively. Each of these rotations, and their composition, is an element of the rotation group SO(3), which is topologically RP3. This animation shows a set of three gimbals mounted together to allow three degrees of freedom. When all three gimbals are lined up (in the same plane), the system can only move in two dimensions from this configuration, not three, and is in gimbal lock. In this case it can pitch or yaw, but not roll (rotate in the plane that the axes all lie in).
Revêtement à deux feuillets du ruban de Möbius, homéomorphe à un cylindre. Le ruban de Möbius vient se glisser entre les deux feuillets.

在拓扑学中，拓扑空间X的覆叠空间是一对数据(Y,p)，其中Y是拓扑空间，p: Y \to X是连续的满射，并存在X的一组开覆盖

X = \bigcup_{U\in \mathcal{U}} U

使得对每个U \in \mathcal{U}，存在一个离散拓扑空间F及同胚：\phi_U: U \times F \simeq p^{-1}(U)，而且p \circ \phi_U: U \times F \to U是对第一个坐标的投影。

满足上述性质的p: Y \to X称为覆叠映射。当X连通时，F的基数是个常数，称为覆叠的次数或重数。

空间X的覆叠构成一个范畴\mathbf{Cov}_X，其对象形如p: Y \to X，从p: Y \to X到q: Z \to X态射是连续映射f: Y \to Z，且q \circ f = p。

英语百科

Covering space 覆叠空间

A covering map satisfies the local triviality condition. Intuitively, such maps locally project a
Gimbal lock occurs because any map T3 → RP3 is not a covering map. In particular, the relevant map carries any element of T3, that is, an ordered triple (a,b,c) of angles (real numbers mod 2π), to the composition of the three coordinate axis rotations Rx(a)∘Ry(b)∘Rz(c) by those angles, respectively. Each of these rotations, and their composition, is an element of the rotation group SO(3), which is topologically RP3. This animation shows a set of three gimbals mounted together to allow three degrees of freedom. When all three gimbals are lined up (in the same plane), the system can only move in two dimensions from this configuration, not three, and is in gimbal lock. In this case it can pitch or yaw, but not roll (rotate in the plane that the axes all lie in).
Revêtement à deux feuillets du ruban de Möbius, homéomorphe à un cylindre. Le ruban de Möbius vient se glisser entre les deux feuillets.

In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below. In this case, C is called a covering space and X the base space of the covering projection. The definition implies that every covering map is a local homeomorphism.
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更新时间：2025/6/20 7:15:35