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102 views

### Is a continuous map between smoothable manifolds of the same dimension always smoothable?

(My question is inspired by this math.SE question, whose
negative answer I showed by a dimension-increasing map.)
Is it the case that for all smoothable manifolds $M_0$ and $M_1$ with the same ...

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158 views

### Lipschitz continuity of solution set mapping of a parametric convex optimization problem

I have a parametric convex optimization problem:
\begin{array}{cl}
\underset{x}{\text{minimize}} & f\left(x,z\right)\\
\text{subject to} & g\left(x\right)\leq0
\end{array}
where $x$ is the ...

**2**

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60 views

### Presentation of tree decompositions (and related concepts) in terms of continuous maps?

A tree decomposition of a graph $G$ is commonly defined in terms of a tree $T$ with the following structure:
Each vertex $t \in V(T)$ is associated to a set $X_t \subseteq V(G)$;
The union ...

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104 views

### Is the Poincare action on the Klein-Gordon quantum field strongly continuous?

I am interested in checking continuity property of the Poincare group action on the Klein-Gordon quantum field theory defined over the Minkowski spacetime. Maybe the simplest example of QFT out there.
...

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116 views

### If an upper semicontinuous multivalued map is compact on a set, is it compact on the boundary as well?

I have stumbled upon the following problem during my research:
Let $X$ and $Y$ be Banach spaces, $K\subset X$ nonempty, $F:\overline{K}\rightarrow 2^{Y}$ an upper semicontinuous multivalued map with ...

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14 views

### Oscillation Index of a function which set of discontinuities is countable

In this paper, the authors defined an oscillation index to be $\beta(f)=\sup_{\epsilon >0}{\beta(f,\epsilon)}$, which has something to do with the set of discontinuities of $f$. Also, the author ...

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35 views

### Uniform continuity in the first variable on compacts w.r.t the other variables for a continuous function

It is a notational doubt.
I have seen the following notation in a book for the continuous function $f$:
$f(.,.):\Bbb R^d \times \Bbb R^d \to \Bbb R$ is uniformly continuous in the first argument on ...

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27 views

### continuous extensions of concave functions

Let $N$ be a lattice. For a ring R we denote $N_R := N \otimes R$. My question is the following:
Does a continuous and concave function
\begin{eqnarray*}
f: N_{\mathbb{Q}} \to \mathbb{R}
...

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26 views

### Show that uniform continuity implies stochastic equicontinuity

Let $\Theta$ be a metric space and assume it is compact. Let $W_t: \Omega \rightarrow \mathbb{R}^k$ be a random variable for $t\leq T$. Let $m(.,\theta): \mathbb{R}^k\rightarrow\mathbb{R}^s$. Let ...

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185 views

### Continuity of a function

Let $f\in L^2(\mathbb{R}^3)$ with compact suppport and $z\in\mathbb{C}$. Is the following function continuous for $z\in Q = \{ z : \Re z\in [a,b], \Im \sqrt{z} \in (0,1] \}$:
$$ ...