英语词汇“Covering transformation”是什么意思，翻译、用法及简单造句-英汉双解词典-英汉网

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单词	Covering transformation
释义	Covering transformation 中文百科覆叠空间 Covering space （重定向自Covering transformation）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（重定向自Covering transformation） 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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