请输入您要查询的英文单词：

　

单词 Connex set
释义

Connex set

中文百科

连通空间 Connected space

（重定向自Connex set）
R² 的连通和不连通子空间。上面的空间 A 是连通的，下面的空间 B 是不连通的。
R² 的这个子空间是道路连通的，因为在这个空间的任何两点之间可绘制一个道路。
Connected and disconnected subspaces of R²From top to bottom: red space A, pink space B, yellow space C and orange space D are all connected, whereas green space E (made of subsets E1, E2, E3, and E4) is not connected. Furthermore, A and B are also simply connected (genus 0), while C and D are not: C has genus 1 and D has genus 4.
Examples of unions and intersections of connected sets

拓扑空间X称为是连通的。当且仅当以下叙述之一成立：

  • X不能表示为两个不相交的非空开集的并集。
  • ∀A⊆X，A≠X或∅，A∩(X-A)≠∅。

一个拓扑空间被称为是不连通的，若它不是连通的。

连通性是拓扑空间的一个拓扑不变性质，即两个拓扑空间之间若存在一个同胚映射，其中一个空间是连通的，则另一个空间也是连通的。

一些数学家承认空集(按照它独有的拓扑)是连通空间，不过也有数学家不承认这一点。

英语百科

Connected space 连通空间

（重定向自Connex set）
Connected and disconnected subspaces of R²From top to bottom: red space A, pink space B, yellow space C and orange space D are all connected, whereas green space E (made of subsets E1, E2, E3, and E4) is not connected. Furthermore, A and B are also simply connected (genus 0), while C and D are not: C has genus 1 and D has genus 4.
This subspace of R² is path-connected, because a path can be drawn between any two points in the space.
Examples of unions and intersections of connected sets
Each ellipse is a connected set, but the union is not connected, since it can be partitioned to two disjoint open sets U and V.

In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets. Connectedness is one of the principal topological properties that is used to distinguish topological spaces. A stronger notion is that of a path-connected space, which is a space where any two points can be joined by a path.
随便看

　

英汉双解词典包含3607232条英汉词条，基本涵盖了全部常用单词的翻译及用法，是英语学习的有利工具。

　

Copyright © 2004-2022 Newdu.com All Rights Reserved
京ICP备09058993号 更新时间：2025/5/14 4:41:08