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单词 Connected space
释义

Connected space

原声例句
Vox 观点

The bungalow interiors feature relatively open floor plans like this: no long hallways, just connected spaces.

没有长长的走廊,只有相连接的空间。

当月 VOA Special English

Surrounded by eight stone walls as tall as 1.7 meters high, the inner structure is divided into smaller, connected spaces.

由八堵高达1.7米的石墙环绕,内部结构被划分成更小的连接空间。

彭博洞察

What we're moving towards now is more the way of the world works: connected spaces.

我们现在正在朝着世界运作的方式迈进:互联空间。

中文百科

连通空间

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

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.

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更新时间:2025/6/22 2:35:24