Tagged Questions
0
votes
0answers
18 views
How to visulize surface link in four dimension?
I am now facing a problem with "surface link" in four dimension. I have heard that three 2-torus can be linked in four dimension. And I have created a movie by cutting four dimensional space with ...
4
votes
1answer
79 views
The complement of a torus is a torus.
Take $S^3$ to be the three-sphere, that is, $S^3=\lbrace (x_1,x_2,x_3,x_4):x_1^2+x_2^2+x_3^2+x_4^4=1\rbrace$. Using the stereographic projection, $S^3=\mathbb{R}^3\cup \lbrace \infty \rbrace.$ Can ...
1
vote
0answers
87 views
Which space this space drawn in this picture is homeomorphic?
Based in this question Why this space is homeomorphic to the plane? I would like to know which space this space is homeomorphic, any help or an intuitive idea are welcome.
[Context of Image: ...
6
votes
2answers
869 views
This quotient space is homeomorphic to the Möbius strip?
Let $G:\mathbb R \times [-1,1]\to \mathbb R \times [-1,1]$ be a map defined by $G(x,y)=(x+1,-y)$
This space $Q=\mathbb R\times [-1,1]/\sim$, where $(x_1,y_1)\sim (x_2,y_2)$ if and only if there is ...
2
votes
1answer
198 views
Visualizing Infinity discerning countable and uncountable
This is rather a philosophical question. Although it uses topological notions, it isn't any precise mathematics, so maybe one cannot take it very seriously.
Sometimes I try to picture an infinite set ...
10
votes
2answers
262 views
What are all these “visualizations” of the 3-sphere?
a 2-sphere is a normal sphere. A 3-sphere is
$$
x^2 + y^2 + z^2 + w^2 = 1
$$
My first question is, why isn't the w coordinate just time? I can plot a 4-d sphere in a symbolic math program and ...
13
votes
3answers
883 views
Cutting a Möbius strip down the middle
Why does the result of cutting a Möbius strip down the middle lengthwise have two full twists in it? I can account for one full twist--the identification of the top left corner with the bottom right ...
5
votes
2answers
381 views
How to Visualize points on a high dimensional (>3) Manifold?
Are there any ways to visualize(plot/draw) points on a high dimensional (ex: dimension = 5) manifold?
