# Questions tagged [mapping-space]

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### Path component of the mapping spaces $G(S^m, S^n)$

Let a non trivial $\alpha\in \pi_m(S^n)$ with a finite order $|\alpha|$. Write $G_\alpha(S^m, S^n)$ for the path-component determined by $\alpha$ of the mapping space $G(S^m, S^n)$ of free maps. Next,...
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1 vote
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### Finding the set of best approximation

Given $X$=$l^1$ and its dual space $X^*=l^\infty$. Now take $f=(1, 1/2, 2/3, 3/4,...) \in X^*$. Then clearly $\|f\|_\infty = 1$. I have found that $H=\ker f$ is a proximinal hyperplane in $X$. Note: A ...
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### Mapping between pseudosphere and breather segments

The pseudospheres $(K=-1)$ shown contain two cuspidal edge boundaries and appear to admit isometric mapping between 1) the surface of revolution through an expansion/contraction deformation in ...
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### Topologies in $\mathcal{C}^\infty(M,N)$

Naively, one could topologise the set of smooth (ie $\mathcal{C}^\infty$) maps between two smooth manifolds $M \to N$ with the subspace topology $\mathcal{C}^\infty(M,N) \subseteq \mathcal{C}^0(M,N)$, ...
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### Does the continuous mapping space between topological manifolds always admit a Banach manifold structure?

Let $M$ and $N$ be smooth, i.e. $C^\infty$, manifolds. Suppose that $M$ is compact. Then for every $k \geq 0$ it is well known that $$C^k(M,N)$$ admits the structure of a smooth Banach manifold. I am ...
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### Can we construct a surjective mapping from $\mathbb{R}^{?}$ to this space?

(Note : I'm not sure about the tags, please re-tag this if you think you have the right tag). I am optimising a certain function over a certain space (that i will describe), and to use non-constraint ...
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### Conformal map onto a circle, from an identification space composed of five squares

I am looking to derive a conformal map for the problem illustrated in this image. I've read a bit about how to map a square onto a circle, but I'm struggling to extend the concepts for the domain at ...
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### Stability for mapping class groups, spaces of sections, and polynomial coefficient systems

Let $X$ be a simply connected space. Cohen and Madsen https://arxiv.org/abs/math/0601750 proved that the functor sending a surface with boundary M to $H_i(Map(M,X))$ has polynomial degree $\leq i$. ...
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### Are morphisms of parametrized spectra themselves parametrized morphisms of spectra?

Let $X$ be a fixed parametrizing space. Let $E$ and $E'$ be two spectra and let $E_X$ and $E'_X$ be their trivial parametrized versions. Intuitively I imagine that the morphisms of parametrized ...
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### Is the Haversine Formula or the Vincenty's Formula better for calculating distance?

Which is better for calculating the distance between two latitude/longitude points, The Haversine Formula or The Vincenty's Formula? Why? The distance is obviously being calculated on Earth. Does ...
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