<em id="zlul0"></em>

<dl id="zlul0"></dl>
<div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
<em id="zlul0"></em>

<div id="zlul0"><ol id="zlul0"></ol></div>

# Questions tagged [continuity]

The tag has no usage guidance.

97 questions
Filter by
Sorted by
Tagged with
102 views

Suppose that $(X,d)$ is a Polish metric space and $A$ is a set of continuous bounded functions $f:X\to \mathbb{R}$. Suppose that $\mu:X\to[0,1]$ is a Borel probability measure. Define \sup A:X\to ... 1answer 155 views ### Continuity of subharmonic functions There is a result saying that the set where a subharmonic function defined on an open set of \mathbb{R}^{m} (m\geq2) is discontinuous is a polar set. Could someone give me a reference for this ... 0answers 74 views ### Maximum theorem with linear constraints. On parametric continuity of in optimization Given \begin{align} s(\theta)= &\text{arg min}( g( \boldsymbol{x}) ) \\ \text{subject to }& \boldsymbol{A}(\theta) \boldsymbol{x} = \boldsymbol{b}(\theta) \\ &c_1 \le x_i \le c_2 , ... 1answer 263 views ### Injective uniformly continuous function f:\mathbb{Z}\times \mathbb{Z}\to \mathbb{Z}? [closed] We say that a function f: \mathbb{Z}\times \mathbb{Z}\to \mathbb{Z} is uniformly continuous if there is an integer K\geq 1 such that whenever (x,y),(x',y')\in \mathbb{Z}\times \mathbb{Z} with |... 1answer 180 views ### “Uniformly continuous” environment sum of a bijection \varphi:\mathbb{Z}\times \mathbb{Z} \to \mathbb{Z} Given any function f: \mathbb{Z}\times \mathbb{Z}\to \mathbb{Z} we define the environment sum of (x,y)\in\mathbb{Z}\times \mathbb{Z} with respect to f by\text{es}_f(x,y) = \sum\{f(x', y'): |(...
144 views

### Reference Request: Stone-Weierstrass on Other Topologies

Let $X$ be a compact subset of $\mathbb{R}^n$. The classical Stone-Weierstrass theorem describes dense subsets of $C(\mathbb{R}^n,\mathbb{R})$ when it is equipped with the compact-open topology. ...
57 views

### What are the various kinds of graphs that can be defined on $C(X)$

I was considering the space $C(X)$ where $X$ is a topological space and $C(X)$ is the set of all continuous functions from $X$ to $\Bbb R$. What are the various kinds of graphs that can be defined on ...
80 views

### Continuity of a constrained parameterized convex optimization problem

Consider the parameterized optimization problem: \begin{align} \boldsymbol{s}(p)= &\arg \min_{ \boldsymbol{x}} \quad g( \boldsymbol{x})\\ \text{s.t. } & \boldsymbol{A}(p) \textbf{x} = \...
101 views

### Continuity of the Restriction Map Between Function Spaces [closed]

Let $X,Y,Z$ be Hausdorff spaces and suppose that $Z\subset X$. Endow $C(X,Y)$ and $C(Z,Y)$ with the compact-open topologies and define the map $\rho$ as \begin{align} \rho:&C(X,Y)\rightarrow C(Z,...
55 views

### Continuity of a continuous time martingale

Consider a Brownian motion $(B_t)_{t\ge 0}$ and its natural filtration $\sigma(B_t)$. Suppose $y_t$ is a $[0,1]$ valued, $\sigma(B_t)$ martingale. Does $y_t$ have continuous sample paths? If not, I ...
80 views

### Continuity of the derivations from semisimple Banach algebras

Let $A$ be a Banach algebra and $X$ a Banach $A$-bimodule. It is known that if $A$ is a $C^*$-algebra, then by Ringrose theorem every derivation $D:A\rightarrow X$ is continuous. Also, a famous ...
65 views

I want to determine what the closure of $C_b^1(\mathbb{R})$, the space of continuous differentiable functions with bounded derivative, with respect to the supremums norm is. I think that \overline{... 1answer 122 views ### Continuity of a parameterized convex optimization problem I have a parameterised optimization problem: \begin{align} \boldsymbol{S}(p)= &\arg \min_{ \boldsymbol{x}} g( \boldsymbol{x})\\ \text{s.t. } & \boldsymbol{A}(p) \textbf{x} = \... 1answer 160 views ### Can a bijection between function spaces be continuous if the space's domains are different? It is well-known that any bijection\mathbb{R} \rightarrow \mathbb{R}^2$cannot be continuous. But suppose we have the two spaces$A = \{f(x):\mathbb{R^2}\rightarrow \mathbb{R} \}$and$B = \{f(x):\...
239 views

### Smallest Lipschitz Constant of a Differentiable Function [closed]

Let $X \subset \mathbb{R}^{n}$ be compact and convex. Moreover, let $f:X \rightarrow \mathbb{R}$ be a differentiable map with $\sup_{x \in X} \|\nabla f(x)\| = K < \infty$, where $\|\cdot\|$ ...

15 30 50 per page
山西福彩快乐十分钟

<em id="zlul0"></em>

<dl id="zlul0"></dl>
<div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
<em id="zlul0"></em>

<div id="zlul0"><ol id="zlul0"></ol></div>