Tagged Questions
2
votes
1answer
93 views
Metric tensor of complex numbers & Hamiltonian Mechanics
The Euclidean $\mathbb{R}^2$ geometric space can be mapped onto $\mathbb{C}$.
In other words I see it like this
$$\vec{v} = x\vec{x}+y\vec{y} = x\vec{1}+y\vec{i}= \begin{bmatrix}x \\y\end{bmatrix} ...
1
vote
1answer
98 views
which of the following are homeomorphic?
well, I have forgotten how to identify ellipse, hyperbola,circle straightline from the general equation of conic, so is there any other way to identify these homeomorphic or not?
a) B is an ellipse, ...
4
votes
3answers
112 views
Points at integer distance
How many points can one can place in $\mathbb{R}^n$, with the requirement that no $n+1$ points lie in the same $\mathbb{R}^{n-1}$-plane, and the euclidean distance between every two points is an ...
3
votes
1answer
122 views
Hausdorff distance vs. distance of the boundaries
I'm tagging this question homework because I'm more interested in hints than in complete solutions. First let us give a definition.
Definition Let $X$ be a metric space. For all $F \subset X, \rho ...
