Recent content by Sumanta

Hi, Actually I think daveyp225 understood my question. Suppose u have a finite product of groups say \Pi G_{i} where the index set is finite. And needless to say there exists from each of these a homomorphism g_{i} to H. So now u could define g: \Pi G_{i} to H as \Sigma...

Hi, I understand the fact that grp theory textbooks defined Hom(G, H) as (g + h) u forms a group homomorphism. I wanted to know if there is any notion of homomorphism as \Sigma_{I} g_{i} where each g_{i} is a homomorphism and I is an infinite index set. If so how is it defined. Thx

Hi, I thought about the problem and I think this could be thought of as a way of thinking. So what we need is the following. Given data: f_{i}: X_{i}\stackrel{injective}{\rightarrow} P g_{i}: X_{i} \stackrel{homomorphism}{\rightarrow} X Now define in someway g: P...

Hi , I was trying to understand why or where would the problem arise in the definition of the direct sum for the coproduct/direct sum for the set (1, 1, 1, ...) infinite number of times. I was trying to reason out as follows. I posted this on the set theory but I am not sure how to tag it to...

Hi, I was trying to understand coproduct and product as defined in category theory from the website http://en.wikiversity.org/wiki/Introduction_to_Category_Theory/Products_and_Coproducts. Before I could even think of sth difficult there are some simple things which I don't seem to...

Hi, I am trying to understand the concept of tangent map and following the ebook of S S Chern. I am a bit confused about the derivation of the tangent map acting on the basis I tried for sometime to type out the equation but it appears I am having problems with the display and not sure what is...

Hello, Could somebody please point me out introductory online book/paper with which I can start understanding gauge theory and how to find out about the progress in the areas Thx

Hello, I am reading the book on algebraic topology by Fulton and the geometric intusion that is supposed to be given for homological group is the number of connected components. I wanted to understand an example. For a circle ( S1) which has got 2 points say A at ( 1, 0) and another...

Hi, Sorry for the misunderstanding. Yes C is the closure of R. Since I was trying to think geometrically so I thought a similar thing is possible in R^3 vs R. So if E is not R^3 but say the field generated by the linear combination of the roots the solution of x^3 - 2 = 0. and the field F is Q...

Hello, I was doing self studying abstract algebra from the online lecture notes posted by Robert Ash and I hit against the following theorem. I am posting it in the topology section because without a geometric/topological meaning to the concept I am never able to understand the topic and that...

Hello, Can somebody pls explain to me what is the difference between generating random numbers and random variables. The confusion is mainly because most of the time texts write that for n (iid) random variables in the limiting sense reaches the expectation of the first random variable. I...

Hi, I say L is not defined because of the following. Let's give an example. Since L can be d^2/dx^2 + a(x) d/dx + b(x) and if u consider the function u s.t for say (a< x <b), a<0, b >0 u(x) = 0 x<0, = x x>= 0 The fn u is cont but is not differentiable at x = 0. So I am not...

Hello, I was trying to understand Green's function and I stumbled across the following statements which is confusing to me. I was referring to the following site http://www.math.ohio-state.edu/~gerlach/math/BVtypset/node79.html Here the author says the following "What if $ u$ is...

Hi , What is understandable is the following v in basis B -----------> v in basis B' -------------> W(on application of T) v is in B and so Pv takes it to another basis in B' so T(v) w.r.t basis B' is nothing but T (Pv) with respect to basis B. q1. Can u apply T to a vector on...

Hello this is not a new thread but a continutaion of the thread of 6th april which I posted. I do not know how to continue the thread and so was not sure and so started as a new topic again. Please refer to my last post also. This is regarding P(Tv) where T is the transfromation from V -> W...