Recent content by seydunas

Hi, Let U be an open subset of R^n and n=>2 and x /in U. I want to show that (n-1)th de rham cohomology of U\ {x} is non zero. I suppose i can solve this question by using excision theorem from singular homology. But i have a hint for this problem: Consider the restrictions S--->U\ {x}---->...

Ok, this question is in the chapter 7 in Lee's book( this is the submersion, immersion chapter). What is the relation of invariance of domain and chapter 7? Why did the auther ask this question at chapter 7?

Sorry, This is not true. It will be R^n can not be homeomorphic to upper half plane. Note that upper half plane is {x=(x_1,,,,,x_n) \in R^n : x_n =>0}.

Hi, I want to show that the set of boundary points on a manifold with boundary is well defined, i.e the image of a point on a manifold with boundary can not be both the interior point and boundary point on upper half space. To do this, it is enough to show that R^n can be homeomorphic to...

Hi, i can not understand how circle has a nontrivial bundle, Möbius bundle. Can you say me what is its transition function on it.

Sorry, our map is linear. So this is true for vector spaces. Now i understood everything.

I can see why ker(phi)=F²_p. But the first isomorphism theorem of algebra is valid for groups, right? Ohh yes, every vector space has a group structure under addition. So, we are done.

Hi, I want to ask a problem from Lee ' s book Introduction to Smooth Manifolds: Let F_p denote the subspace of C^\inf(M) consisting of smooth functions that vanish at p and let F^2_p be the subspace of F_p spanned by functions fg for some f,g \in F_p. Define a map \phi: F_p----->...

i just want to ask what are the functions whose cube is smooth?

If we can take the interior of support coming from partition of unity, we are done.

Hi, I want to charectize the function whose cube is smooth from R to R. For example x^1/3 is smooth and olsa any polynomial but how can i charectrize it? Thanks

Hi, i have tried to solve exercise2.16 in Lee' s book, smooth manifolds: Let X be a top. mfd with the propert that for every open cover O there exist partition of unity subordinate to O. Show X is paracompact. I think there is a trick to construct locally refinement open cover by using...

Sorry quasar, but how can sure that you can modify the atlas A to A' as you describe before?. In my opinion, we can write function f: B^n---> B^n s.t x--->x.absvalue(x)^-2/3, this map is homeomoprhism and it is not differentiable at 0. Now, if we compose it by g which is taken at first, we get...

For manifold with boundary, how can we write the charts precisely?

C/inf(M) is infinite dimensional but how? I thought that for all point on M (one point is closed set) there exist open nhd, and by using partitions of unity we can extend the function on M , now i wonder that the set of theese functions is linearly independent or not? IF so, we are done.