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dxbkky

金虫 (小有名气)


[交流] 【求助】拓扑数学题求助

有一套拓扑方面的数学题,请求虫友帮忙!急,重赏80金


1.Please prove that“f  homotopic to g”is an equivalence relation for functions f,g :
X → Y .
2.Please prove that“X is homotopic to Y ”is an equivalence relation for spaces X and
Y .
3.A starlike space S ⊂ Rn is a subspace S of Rn that satisfies the followin gproperty:
there exists a point s ∈ S sothat for every point x ∈ S,there is a straight line path
from x to s.Please prove thate very starlike space S is contractible.(Rn中n为上标)
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sdlmm

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引用回帖:
Originally posted by dxbkky at 2011-02-15 10:07:53:
有一套拓扑方面的数学题,请求虫友帮忙!急,重赏80金


1.Please prove that“f  homotopic to g”is an equivalence relation for functions f,g :
X → Y .
2.Please prove that“X is homotopic to Y ” ...

1.验证3条,对称,反身,传递性。特别是第三条传递性的时候要把两个连接函数拼在一起。

2.两个空间是同伦等价的,重点也是在于第三条,需要复合同伦等价映射就可以了。
3.就是星形区域了,hoho,都道路连通了啊,还不可缩吗。。。。。


o(╯□╰)o
2楼2011-03-17 22:51:36
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