请教几道以前的考题，谢谢！

ballack13UID: 2494001

１．Let G be the group of symmetries of the regular pentagram，then G is isomorphic to :

1. S_5
2. A_5
3. a cylic group of order 5
4. a cylic group of order 10
5. dihedral group of order 10


这个题目怎么做啊？这到底是考查哪方面的知识？拓扑？哪本书上有这方面知识的讲解？谢谢！

２．which letter is not homeomorphic to the letter C?
Ａ.J B.N C.S D.O E.Ｕ
见过有人用基本群的观点解答，但由于我能力有限，各位高手能否说的详细一点？谢谢了．

3.R^n中一个紧连通集的补集的连通分支最多几个？
这个题有没有一个统一的意见啊？哪位高手能解释一下？

见

landafrankUID: 2476087

1.选最后一个 二面体群 这是抽代的知识
2.选D，不用多想，你就把所有的字母想象成可以拉伸的橡皮泥 哪个可以拉成letter C，哪个就是homeomorphic的
3.不明白 同问

soarerzUID: 2721318

2. Other than D, the other options can all be shrunk to a point.

3. It has to be unbounded. Take a circle with n holes, then the complement has n+1 connected components.

prettywraithUID: 197049

to楼上：
3，关于连通分支我在wikipedia上查的好像是说 有两个，一个是分支是有界，一个是无界。图论这部分没什么概念，比较糊涂，楼上能否解释的详细点。多谢！

soarerzUID: 2721318

this is not graph theory but topology, and what is not clear about what I have said..? Did I misunderstand the question..?
Or maybe we can use squares instead. The complement of a square with two holes have 3 connected components (the two holes and the unbounded part). 3 holes => 4 connected components, and so forth.

prettywraithUID: 197049

呵呵，哦，我理解成连通图。 不过你说的这部分我也没看过。学习了先。

lossingzoneUID: 2519545

第三题是无穷，正如soarerz所说，挖无穷的洞即可