# All Questions

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### Radial limit does not exist almost everywhere

Problem 4 in Chapter 4 of Stein's book "Real Analysis" says $\sum_{n\geqslant 0}z^{2^n}$ doesn't have radial limit as $z$ approaches the unit circle from inside almost everywhere. It's fairly easy ...
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### cobordism and smoth-manifold

Let M, N , N' and M' be smooth n-manifolds with nonempty boundaries , and suppose h:∂M→∂N , g:∂M'→∂N' are diffeomorphisms . Let M∪_h N be the adjunction space formed by identifying each xϵ∂M with ...
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### Multi-podal points

Two points $x,y \in \mathbb{R}^n$ are called antipodal if $x = -y$. Stated differently, $x,y$ are antipodal if: They have the same absolute value in each of their $n$ coordinates; Each of their ...
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### How does one express a Lagrangian via differential forms? [duplicate]

I asked this question here on Physics.SE; and I accepted an answer, which thinking about it later I was dis-satisfied with; to save clicking on the link I'm reproducing the question below: In ...
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### Automorphisms of a differential field and transcendence degree

Let $(\mathcal{F},+,\times,\partial)$ be a differential field, and let's define its automorphism group $Aut(\mathcal{F})$ as the group, under composition, consisting of all bijective maps ...
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### Uniform space structures of different metric on the same space

I started learning about uniform spaces and I got confused with the uniform structures and its relation to metric spaces. I am not sure when different metric structures on the same space produce ...
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### Schubert Calculus for Quaternion-Kähler Manifolds

The cohomology ring of general Grassmannians have very nice presentations in terms of Young diagram and the rules of Littlewood-Richardson. This is called {\em Schubert calculus}. The Grassmannian of ...
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### Is every $C^1$-domain which is homeomorphic to the unit ball in $\mathbb{R}^d$ Lipschitz equivalent to the unit ball?

Suppose we have a domain $\Omega\subset \mathbb{R}^n$ which is homeomorrphic to the unit ball $B(0,1)\subset \mathbb{R}^n$ and such that $\partial \Omega$ is of class $C^1$ (technically, this means ...

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