Questions tagged [continuous-geometry]
Use this tag for questions about lattices whose subspace dimensions can be a number in the interval [0, 1].
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On motivations of continuous geometry
The development of continuous geometry as an abstract field seems to be following a trend of removing the significance of low-dimensional entities from geometry. As classical treatments of geometry ...
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Playing tag with infinitely many friends
All the countably infinitely many guests of Hilbert's Hotel decide to spend the day playing tag in the park. One player is the runner, and all the others are it. The taggers can agree on a strategy ...
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expected value from some points in continuous homogeneous spatial Poisson point process
Let $n$ point are distributed as per a homogeneous spatial Poisson process of rate $λ$ in a square of side $2a$, and assume that $4$ fixed points are located at $(\frac{a}{2},\frac{a}{2})$, $(-\frac{a}...
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There is a natural set of numbers with dimension in [0,1]?
After reading this question, I want to know: if $\mathbb{Z}$ is $\mathbb{R}^0$ (according to Hausdorf Dimension of the integer set), and $\mathbb{R}$ is $\mathbb{R}^1$, there is a natural definition ...
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Fitting a straight line and a curve (hypocyloid) with C2/C1 continuity (problem at joints)
(Kindly have a look at the link of the picture in the link)
I am joining a straight line, a hypocycloid curve (in between), and a straight line again, which are joined arbitrarily. At the point of ...
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Prove that a group law of the Heisenberg group is continuous.
The group law on $\mathbb{H}^n$ -Heisenberg group- is given as follows:
$(s,x,y)·(s′,x′,y′)=(s+s′+ ω(x,y;x′,y′),x+x′,y+y′)$,
how can I prove that this group law is continuous?
Many thanks.
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Proof that any curve in two dimensions has a modelling differential equation.
I was wondering if anyone knew of a proof stating that any smooth, continuous line drawn in two dimensions must have a differential equation that models it.
Best,
James.
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Least upper bound and greatest lower bound of the void set.
Let $(L,\ge)$ a partially ordered set. Suppose that for avery $S \subset L$, there exists an element $LUB(S)= a$ such that $x \ge a \iff x \ge u \quad \forall u \in S$ and, with the obvious meaning of ...
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