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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|拓扑学代写Topology代考|SPACES OF CONTINUOUS FUNCTIONS

In Example 9-5 we gave a brief description of the metric space $\mathcal{e}[0,1]$. The reader will recall that the points of this space are the bounded continuous real functions defined on the closed unit interval $[0,1]$ and that its metric is defined by $d(f, g)=\sup |f(x)-g(x)|$. We have two aims in this section: to generalize this very important example by considering functions defined on an arbitrary metric space, and to place all function spaces of this type in their proper context by giving the details of the structural pattern (discussed briefly in Sec. 9) which they all have in common with one another. We begin with the second, and define the algebraic systems which are relevant to our present interests.

Let $L$ be a non-empty set, and assume that each pair of elements $x$ and $y$ in $L$ can be combined by a process called addition to yield an element $z$ in $L$ denoted by $z=x+y$. Assume also that this operation of addition satisfies the following conditions:
(1) $x+y=y+x$
(2) $x+(y+z)=(x+y)+z$;
(3) there exists in $L$ a unique element, denoted by 0 and called the zero element, or the origin, such that $x+0=x$ for every $x$;
(4) to each element $x$ in $L$ there corresponds a unique element in $L$, denoted by $-x$ and called the negative of $x$, such that $x+(-x)=0$.

We adopt the device of referring to the system of real numbers or to the system of complex numbers as the scalars. We now assume that each scalar $\alpha$ and each element $x$ in $L$ can be combinèd by a prōcéss cällèd scalar multiplication to yield an element $y$ in $L$ denoted by $y=\alpha x$ in such a way that
(5) $\alpha(x+y)=\alpha x+\alpha y$;
(6) $(\alpha+\beta) x=\alpha x+\beta x$;
(7) $(\alpha \beta) x=\alpha(\beta x)$;
(8) $1 \cdot x=x$.

## 数学代写|拓扑学代写Topology代考|EUCLIDEAN AND UNITARY SPACES

Let $n$ be a fixed positive integer, and consider the set $R^{n}$ of all ordered $n$-tuples $x=\left(x_{1}, x_{2}, \ldots, x_{n}\right)$ of real numbers. ${ }^{2}$ We promised in Sec. 4 to make this set into a space, and we are now in a position to do so.
1 The construction outlined in (a) to (c) clearly depends on the initial choice of the fixed point $x_{0}$. If another fixed poin: $x_{0}$ is chosen, then another isometry $F$ of $X$ into $e(X, R)$ is determined. It would seem, therefore, that there is little justification for calling the particular $X^{}$ defined in this problem the completion of $X$. In practice, however, we usually pursue the reasonable course of regarding isometric spaces as essentially identical. From this point of view, the $X^{}$ defined here is a complete metric space which contains $X$ as a dense subspace; and since by $(h)$ it is the only complete metric space with this property, it is natural to call it the completion of $X$.
“From this point on, we omit the adjective “ordered.” It is to be understood that an $n$-tuple is always ordered.

We begin by defining addition and scalar multiplication in $R^{n}$. If $x=\left(x_{1}, x_{2}, \ldots, x_{n}\right)$ and $y=\left(y_{1}, y_{2}, \ldots, y_{n}\right)$, then we define $x+y$ and $\alpha x$ (where $\alpha$ is any real number) by
and
\begin{aligned} x+y &=\left(x_{1}+y_{1}, x_{2}+y_{2}, \ldots, x_{n}+y_{n}\right) \ \alpha x &=\left(\alpha x_{1}, \alpha x_{2}, \ldots, \alpha x_{n}\right) . \end{aligned}
With the algebraic operations defined coordinatewise in this way, $R^{n}$ is a real linear space. The origin or zero element is clearly $0=(0,0, \ldots, 0)$; and the negative of an element $x=\left(x_{1}, x_{2}, \ldots, x_{n}\right)$ is
$$-x=\left(-x_{1},-x_{2}, \ldots,-x_{n}\right) \text {. }$$
When we speak of $R^{n}$ as an $n$-dimensional space, all we mean at this stage is that each element $x=\left(x_{1}, x_{2}, \ldots, x_{n}\right)$ is the ordered array of its $n$ coordinates $x_{1}, x_{2}, \ldots, x_{n}$.

# 拓扑学代考

## 数学代写|拓扑学代写Topology代考| SPACES OF CONTINUOUS FUNCTIONS

(1) $x+y=y+x$
(2) $x+(y+z)=(x+y)+z_{i}$
(3) 存在于 $L$ 个唯一的元素，用 0 表示，称为零元素或原点，使得 $x+0=x$ 对于每个 $x$;
(4) 到每个元素 $x$ 在 $L$ 有对应的唯一元素 $L$ ，表示为 $-x$ 并称为负数 $x$ ，使得 $x+(-x)=0$.

(5) $\alpha(x+y)=\alpha x+\alpha y$;
(6) $(\alpha+\beta) x=\alpha x+\beta x$;
(7) $(\alpha \beta) x=\alpha(\beta x)$;
$(8) 1 \cdot x=x$

## 数学代写|拓扑学代写Topology代考| EUCLIDEAN AND UNITARY SPACES

1 (a) 至 (c) 中概述的结构显然取决于不动点的初始选择 $x_{0}$ 如果另一个固定的 poin： $x_{0}$ 被选中，然后选择另一个等轴测 $F$ 之 $X$ 到 $e(X, R)$ 已确定。因此，似 乎没有理由称其为特定 $X$ 定义在这个问题中完成 $X$. 然而，在实践中，我们通常追求合理的过程，将等距空间视为本质上相同的空间。从这个角度来看， $X$ 这里 定义的是一个完整的度量空间，其中包含 $X$ 作为密集的子空间;并且由于由 $(h)$ 它是唯一具有此属性的完整度量空间，自然而然地将其称为完成 $X$. “从这一点开始，我们省略了形容词’有序’。应当理解，一个 $n$-元组始终有序。

$$x+y=\left(x_{1}+y_{1}, x_{2}+y_{2}, \ldots, x_{n}+y_{n}\right) \alpha x \quad=\left(\alpha x_{1}, \alpha x_{2}, \ldots, \alpha x_{n}\right) .$$

$$-x=\left(-x_{1},-x_{2}, \ldots,-x_{n}\right) .$$

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

assignmentutor™您的专属作业导师
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