# Questions tagged [pushforward]

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### Uniform Continuity and Mass of Pushforward

Let $(X,d)$ be a metric space and $m$ be a regular Borel measure on $(X,d)$. Let $(Y,\rho)$ be another metric space and $f:X\rightarrow Y$ be a uniformly continuous function with increasing ...
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### Inverse push-forward on RKHS

I am considering an infinite dimensional separable RKHS $H$ of functions from $E$ to $\mathbb{R}$, where $E$ is any measurable space. I denote by $\phi:E \rightarrow H$ the canonical feature map of $H$...
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### Push-forward of a smooth function

I'm confused about the relation between two concepts: the push-forward of a smooth map between two smooth manifolds and the differential of a smooth real-valued function. Let $M,N$ be smooth manifolds ...
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### Differential of a smooth covering map is always invertible?

If $f: E \to M$ is a smooth covering map between manifolds, is it true that the differential (or the push-forward) $df_p : T_p E \to T_{f(p)}M$ is invertible for every $p\in E$? I think this should be ...
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### Proving a Covariant Derivative is Torsion Free

Let $(M,g)$ be a metric manifold and $\phi:M\to N$ a diffeomorphism, where $N$ is another manifold. Let $\nabla$ be the Levi Civita connection with respect to the metric $g$, and we define a ...
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Having some difficulty with the following proposition, Consider a $C^\infty$ map between manifolds $F:N \rightarrow M$ with $\text{dim} \, N = \text{dim} \, M$, then $F$ is locally invertible ...