topology
简明释义
n. 拓扑学
复 数 t o p o l o g i e s
英英释义
单词用法
[计]网络拓扑结构 | |
[计]拓扑结构 |
同义词
反义词
无序 | The disorganization of the files made it hard to find important documents. | 文件的无序使得很难找到重要的文件。 | |
混乱 | 聚会期间房间里的混乱让人感到不堪重负。 |
例句
1.Topology is the top-most element of any topology model.
拓扑是任何拓扑模型的最高层元素。
2.Open the runtime environment and create a new topology.
打开运行时环境,并创建一个新的拓扑。
作业管理器拓扑。
4.Install the Topology Domain Generation Toolkit.
安装拓扑域生成工具箱。
5.Add a virtual image unit to the topology.
向拓扑架构添加一个虚拟的图片单元。
6.Proposed topology and run time environment.
推荐的拓扑和运行时环境。
7.The topology of the city was influenced by its historical development and geographical features.
这个城市的拓扑结构受到历史发展和地理特征的影响。
8.In mathematics, the study of topology involves properties that remain unchanged under continuous transformations.
在数学中,拓扑学的研究涉及在连续变换下保持不变的性质。
9.The topology of the dataset can affect the performance of machine learning algorithms.
数据集的拓扑结构会影响机器学习算法的性能。
10.Understanding the topology of a computer network is crucial for effective troubleshooting.
理解计算机网络的拓扑结构对于有效故障排除至关重要。
11.The network's topology is designed to minimize latency during data transmission.
该网络的拓扑结构旨在最小化数据传输中的延迟。
作文
In the realm of mathematics, the concept of topology plays a crucial role in understanding the properties of space that remain invariant under continuous transformations. Unlike traditional geometry, which focuses on the exact distances and angles between points, topology is concerned with the qualitative aspects of space. This means that it studies how objects are connected or related to one another without necessarily measuring their size or shape. For example, a coffee cup and a donut are considered topologically equivalent because they both have one hole; you can transform one into the other through stretching and bending, but not tearing or gluing. The origins of topology can be traced back to the early 20th century, when mathematicians began to explore the ideas of continuity and convergence. The field has since evolved into various branches, including algebraic topology, differential topology, and geometric topology. Each of these branches focuses on different aspects of topological spaces, providing tools and frameworks for analyzing complex structures. One of the most fundamental concepts in topology is that of a 'topological space.' A topological space is defined as a set of points, along with a collection of open sets that satisfy certain axioms. These axioms allow mathematicians to define concepts such as continuity, compactness, and connectedness. Understanding these properties is essential for various applications, from data analysis to physics. In recent years, the applications of topology have expanded beyond pure mathematics into fields such as computer science, biology, and even economics. In data science, for instance, topology is used in the study of persistent homology, a method for analyzing the shape of data. By examining the topological features of datasets, researchers can gain insights into the underlying patterns and structures that may not be immediately apparent. Moreover, in the field of neuroscience, topology helps scientists understand the complex network of connections within the brain. By modeling neural connections as a topological space, researchers can analyze how different regions of the brain interact and communicate, leading to a deeper understanding of cognitive functions and disorders. In conclusion, topology is a fascinating and multifaceted area of mathematics that provides valuable insights into the nature of space and connectivity. Its principles transcend traditional boundaries, finding relevance in diverse fields such as data science, biology, and neuroscience. As we continue to explore the intricacies of our world, the importance of topology will only grow, offering new perspectives and tools for understanding complex systems. Whether in theoretical research or practical applications, the study of topology remains an essential component of modern science, illuminating the relationships that shape our universe.
在数学领域,拓扑学的概念在理解空间的性质方面发挥着至关重要的作用,这些性质在连续变换下保持不变。与传统几何学专注于点之间的确切距离和角度不同,拓扑学关注的是空间的定性方面。这意味着它研究物体如何连接或相互关联,而不一定测量它们的大小或形状。例如,咖啡杯和甜甜圈被认为是拓扑等价的,因为它们都有一个孔;你可以通过拉伸和弯曲将一个变形为另一个,但不能撕裂或粘合。拓扑学的起源可以追溯到20世纪初,当时数学家开始探索连续性和收敛性的思想。该领域自此演变为多个分支,包括代数拓扑学、微分拓扑学和几何拓扑学。这些分支各自关注拓扑空间的不同方面,为分析复杂结构提供了工具和框架。拓扑学中最基本的概念之一是“拓扑空间”。拓扑空间被定义为一组点,以及满足某些公理的开集集合。这些公理使数学家能够定义诸如连续性、紧致性和连通性等概念。理解这些属性对于各种应用至关重要,从数据分析到物理学。近年来,拓扑学的应用已超越纯数学,扩展到计算机科学、生物学甚至经济学等领域。例如,在数据科学中,拓扑学用于研究持久同调,这是一种分析数据形状的方法。通过检查数据集的拓扑特征,研究人员可以深入了解潜在的模式和结构,这些模式和结构可能并不立即显现。此外,在神经科学领域,拓扑学帮助科学家理解大脑内复杂的连接网络。通过将神经连接建模为拓扑空间,研究人员可以分析大脑不同区域如何相互作用和沟通,从而更深入地理解认知功能和障碍。总之,拓扑学是一个迷人且多面的数学领域,为理解空间和连通性的本质提供了宝贵的见解。其原理超越了传统界限,在数据科学、生物学和神经科学等多个领域中找到相关性。随着我们继续探索世界的复杂性,拓扑学的重要性只会增加,为理解复杂系统提供新的视角和工具。无论是在理论研究还是实际应用中,拓扑学的研究仍然是现代科学的重要组成部分,照亮了塑造我们宇宙的关系。