Questions tagged [embeddings]
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184
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Closed regular monomorphism and closed subspace
I have read the categorical definition of embedding, which is that of regular monomorphism. In the case of the category of locally ringed space, is it true that closer subspaces are defined by closed ...
- 67
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Embeddings of Bochner-Sobolev spaces with second time derivative
NOTE: I also asked this question here in MSE.
In the weak theory of evolution PDEs, the Bochner-Sobolev spaces are frequently used. For $a,b \in \mathbb{R}$ and $X,Y$ banach spaces, we define these ...
- 21
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"Almost embedding" the complete 2-dimensional complex $\mathcal K_7^2$ into $\Bbb R^4$
Let $\mathcal K_7^2$ be the complete 2-dimensional simplicial complex on seven vertices, i.e. it has all $7\choose 2$ edges and all $7\choose 3$ 2-simplices (and no higher-dimensional simplices).
I ...
- 12.8k
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Local embedding and disk in domain perturbation
Consider say $M=(\mathbb{S}^1\times\dotsb\times \mathbb{S}^1)-q$ ($n$-times). Assume that $B$ is an $n$ disk in $M$ (for instance, thinking of $\mathbb{S}^1$ as gluing $-1$ and $1$, the cube $B=[-\...
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Is there a variant of the crossing lemma for multigraphs with arbitrary embedding?
Suppose $G$ is a graph embedded in the plane with $m=|E(G)|$ edges and $n=|V(G)|$ vertices.
Suppose $\operatorname{sim}(G)$, the simplification of $G$ contains $ m' \gg 3n $ edges.
Call the set of ...
- 91
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"separators" for nonplanar graphs embedded in the plane
Given a nonplanar graph $G$ drawn in the plane with crossings.
Does there exist a small ($o(|V(G)|$) subset $S$ of edges of $G$ such that after the removal of all edges that intersect or share an ...
- 91
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Constants in the entropy number of the Sobolev space
For a Sobolev space with $W^s(\Omega)$, where $\Omega\subset R^d$ is a compact space with smooth boundary, we know that the entropy number satisfies $e(\delta, W^s(\Omega, 1),\|\cdot\|_{L_\infty})\leq ...
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118
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Embedding of the first Hirzebruch surface in $\mathbb{P}^4$ as a cubic surface
The first Hirzebruch surface (the blow-up of $\mathbb{P}^2$ at one point) is a projective toric surface that naturally embeds into $\mathbb{P}^4$ as a cubic surface (sometimes called the cubic scroll)....
- 173
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Can a closed null-homotopic curve be filled in by a disc?
Let $U\subseteq\Bbb R^n$ be an open set and $\gamma\subset U$ a closed null-homotopic curve in $U$ (i.e. it can be contracted to a point). Then is there an embedded disc $D\subset U$ with boundary $\...
- 12.8k
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Does the continuous image of a disc contain an embedded disc?
Let $\phi:\Bbb D^2\to\Bbb R^n$ be a continuous mapping of the 2-disc $\Bbb D^2$ that is injective on the boundary $\partial\Bbb D^2=\Bbb S^1$. Does its image contain an embedded disc with the same ...
- 12.8k
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Dependence of Sobolev embedding theorem constant on smoothness
Assume that $\Omega \subset \mathbb{R}^d$ is "nice" enough and $k$ is a positive real number. Using the Sobolev embedding theorem, we can get that
$$
\|f\|_{W^{0,2d/(d-2k)}\ \ \ \ \ (\Omega)}...
- 11
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Is it consistent to have an infinite antitone sequence of elementary embeddings such that the involved models include iterated sharps?
$\DeclareMathOperator\crit{crit}$Background essays (the material I've tried to understand in leading up to this question):
Daghighi, et. al. [2014], "The foundation axiom and elementary self-...
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Does $c$ in the embedding inequality $\|P^\kappa_t \|_{L^p \to L^{p'}} \le c t^{-\frac{d(p'-p)}{2pp'}}$ depend on $\kappa$?
For any $\kappa>0$, we consider the Gaussian heat kernel
$$
p^\kappa_t (x) := (\kappa \pi t)^{-\frac{d}{2}} e^{-\frac{|x|^2}{\kappa t}},
\quad t>0, x \in {\mathbb R}^d.
$$
Let $L^0 := L^0 (\...
- 1,179
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Different flavours of Vassiliev Conjecture
There is something that puzzles me about "Vassiliev's Conjecture". I am sure I am missing some detail which is obvious to the community, since there are several tightly related kind of ...
- 1,954
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stating large cardinal axioms in ZF
Can I ask whether there is a good reference for how to state the standard large cardinal axioms in the context of $ZF$? My concern is that it seems that the usual proof that embeddings defined from ...
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