w**********a
发帖数: 107 | 1 R2空间中，一个紧连通的子集的补集，最多有多少连通分支？ 有人给出答案说是无穷
个？ 不明白为什么。 谢谢 |
A****s
发帖数: 129 | 2 画一个大圆,在里面找地方画半径为1/n的小圆？
【在 w**********a 的大作中提到】
: R2空间中，一个紧连通的子集的补集，最多有多少连通分支？ 有人给出答案说是无穷
: 个？ 不明白为什么。 谢谢
|
h*******e
发帖数: 225 | 3 吃过Pretzel吧
【在 w**********a 的大作中提到】
: R2空间中，一个紧连通的子集的补集，最多有多少连通分支？ 有人给出答案说是无穷
: 个？ 不明白为什么。 谢谢
|
w**********a
发帖数: 107 | 4
但是，连通分支的定义是，The maximal connected subsets of any topological
space are called the connected components of the space.Since this subset is
compact and connected, it is closed and bounded. I cann't figure out why
there are more than one connected components of its complement.
【在 h*******e 的大作中提到】
: 吃过Pretzel吧
|
A****s
发帖数: 129 | 5 you first draw a big enough circle, and then cut an open "hole" of radius 1
in its interior, and radius 1/2, 1/4,1/8.... all of these circles are
infinitely many connected components.
is
【在 w**********a 的大作中提到】
:
: 但是，连通分支的定义是，The maximal connected subsets of any topological
: space are called the connected components of the space.Since this subset is
: compact and connected, it is closed and bounded. I cann't figure out why
: there are more than one connected components of its complement.
|
w**********a
发帖数: 107 | 6 got you 3q
1
【在 A****s 的大作中提到】
: you first draw a big enough circle, and then cut an open "hole" of radius 1
: in its interior, and radius 1/2, 1/4,1/8.... all of these circles are
: infinitely many connected components.
:
: is
|
w**********a
发帖数: 107 | 7 高
【在 h*******e 的大作中提到】
: 吃过Pretzel吧
|
