Recent content by andlook

Of course, as defined in the statement of the question! Thanks

Homework Statement Verify that taking \mathbb{R}, the empty set and finite sets to be closed gives a topology. Homework Equations The Attempt at a Solution Clearly the empty set is finite as it has 0 elemnts, and so is closed. If X_i , for i= {1,...,n}, are finite sets then...

Ok so the quotient R/~ = [0,1) for the relation x~x+1? Then defining the map f:[0,1)---S^1 via f(x)=exp(2*Pi*x*i) for x in [0,1). Yes I am working on the definition that open sets in the preimage are open defines continuity and so give definition of homeomorphism. I take by showing that...

for anyone that needs more on this I found extrapolation given by M grime third post down on thread https://www.physicsforums.com/showthread.php?t=124804 At least I found this helpful

Ok thought about this some more. What I have done above is actually on the right path, if the horizontals of the square are identified we get a cylinder, if the vertical height is shrunk to nothing, so we are working in just R, then we get a circle. Then the result follows. I think the...

Homework Statement verify that R, the reals, quotiented by the equivalence relation x~x+1 is S^1 Homework Equations The Attempt at a Solution All i can think of is to draw a unit square and identify sides like the torus, but this would be using IxI, a subset of R^2, and gives a...

Hi I intend to use a interactive program I have written in mathematica in a presentation. But it has become apparent that I may not have internet access when giving this talk, my license only allows me to open mathematica when I am connected to the web. Is there any programs that will allow...

Hi So I'm looking at presentations. I think that I understand that the group that generates <a,b|a^2,b^2> is Z/2 x Z/2. But how can I find out the group, that generates other presentations such as <a,b,c|aba^(-1)bcc>? Thanks

What is a question in topology asking of me when it says show that the topology of S1 and a quotient space agree?

Hi Is graph theory a more pure or applied subject? I thought it was pure but now I am confusing myself because it has so many applications. Thanks

So I want to draw a number of objects on the same picture. The object is defined parametrically: ParametricPlot3D[{Cos[u] Sin[v], Sin[u] Sin[v], Cos[v]}, {u,0,2Pi,Pi/20},{v,0,Pi,Pi/12}, Axes->None, Boxed->False] gives one object. Then Do[ParametricPlot3D[ {Cos[u] Sin[v]...

Hi I have define a 3D object with ParametricPlot3D, something similar to a sphere called "obj." I then want to use a matrix, I define as "move," to translate the object around, I have been trying: obj = ParametricPlot3D... move = AffineTransform[{{1, 1, 2}, {0,1 , 1}, {0, 0, 1}}]...

In differential geometry what does df mean as in \mbox{f} : \mathbb{R}^m \mbox{ to } \mathbb{R}^n Then df is what? the jacobian matrix of partial derivatives?

Hi I've been drawing surfaces in Mathematica but some of the images come out jaggy and very unsmooth. Is there a command that can be added that will increase 'resolution' or smoothness of the surfaces. Thanks

Thanks, that's great. I'm not really sure if this question would be well defined, but how would I then apply this method to the second metric (ds)^2=(dx)^2+(1+x^2)(dy)^2 -2x(dy) +(dz)^2 ?