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5
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0answers
200 views

Topological conditions forcing continuity

Let $X$, $Y$, and $Z$ be topological spaces. Let $f:X \rightarrow Y$. Further assume that for every continuous function $g:Y \rightarrow Z$, $g \circ f$ is continuous. Question: Under what ...
2
votes
0answers
58 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 ...
1
vote
0answers
55 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 ...
1
vote
0answers
106 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 ...
1
vote
0answers
90 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. ...
0
votes
0answers
16 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 ...
0
votes
0answers
26 views

B-spline re-parametrization

I have a question regarding the re-parameterisation of a B-spline. Some info: The B-spline is of order 4 (degree 5), hence $C^3$ continuity There is no knot multiplicity The end conditions are not ...
0
votes
0answers
60 views

Continuity of the real Monge Ampère operator on convex functions

Let $E\subset\mathbb{R}^n$ be a convex set, $u:E\to\mathbb{R}$ a convex function and $B\subset E$ a Borel set. We define the (multivalued) gradient \begin{array}{rccl} \nabla [u]:& \mathbb{R}^n ...
0
votes
0answers
176 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 $z\in Q = \{ z : \Re z\in [a,b], \Im \sqrt{z} \in (0,1] \}$: $$ ...