topologically

简明释义

英[tɒpəˈlɒdʒɪkli]美[tɑːpəˈlɑdʒɪkli]

adv. 拓扑地

英英释义

单词用法

同义词

反义词

例句

1.In chapter 2. we research topologically ergodic maps.

第二章研究了拓扑遍历映射。

2.Using it the scale of electrical networks which can be topologically analysed by a computer will be increased, and the result expressions are terse.

应用它可以扩大一台计算机所能拓扑分析的电网络的规模，而且表达式紧凑。

3.A more general topologically finite intersection property is obtained.

本文研究了更一般的拓扑有限交的性质。

4.MGE contains tools for building and maintaining topologically clean data without the processing and storage overhead of building and maintaining topology.

MGE包含着建立维持拓补清理数据的工具，而不用在建立维持拓补前进行处理和存储。

5.We characterize almost periodicity with equicontinuity, and prove that if the group is uniform equicontinuous then it is topologically equivalent to an isometric one.

本文对一致空间上的群作用，用等度连续性刻画了几乎周期的性质，并且论证了一致等度连续的群作用拓扑等价于一等距的群作用。

6.A general topologically finite intersection property is obtained. As application, we utilize this result to obtain some minimax theorems.

本文得到一个一般的拓扑型有限交性质，并将所得结果应用于研究拓扑型极大极小定理。

7.Topologically Integrated Geographic Encoding and Referencing?

拓扑集成的地理编码和引用TIGER ？

8.The researchers demonstrated that the objects are topologically 拓扑上 invariant under certain transformations.

研究人员证明这些物体在某些变换下是拓扑上不变的。

9.We need to consider how these networks are topologically 拓扑上 connected to optimize performance.

我们需要考虑这些网络是如何拓扑上连接的，以优化性能。

10.In this study, we analyze the topologically 拓扑上 distinct features of the surfaces.

在这项研究中，我们分析了表面的拓扑上不同特征。

11.The data sets are topologically 拓扑上 arranged to facilitate easier comparison.

数据集被拓扑上排列，以便于更简单的比较。

12.The two shapes are topologically 拓扑上 equivalent, meaning they can be transformed into each other without cutting.

这两种形状在拓扑上是等价的，意味着它们可以在不切割的情况下相互转换。

作文

In the field of mathematics, particularly in topology, the term topologically refers to properties that are preserved under continuous deformations such as stretching, twisting, crumpling, and bending, but not tearing or gluing. This concept is essential for understanding the nature of space and how different shapes can be transformed into one another without losing their fundamental characteristics. For example, a coffee cup and a doughnut are considered equivalent topologically because each can be transformed into the other through a series of continuous deformations. This idea challenges our traditional notions of geometry, where shapes are often defined by rigid measurements and fixed points.Topology, as a branch of mathematics, allows us to explore these abstract concepts, leading to insights that have applications in various fields, including physics, biology, and computer science. When we analyze objects topologically, we focus on their intrinsic properties rather than their extrinsic measurements. This perspective has profound implications, especially in understanding complex systems and phenomena.For instance, in the study of networks, whether they are social networks, neural networks, or transportation systems, the topological structure can reveal how information flows, how connections are made, and how resilient the system is to failures. By examining these networks topologically, researchers can identify critical nodes that, if removed, would disrupt the entire system. This insight is invaluable in designing more robust networks and understanding vulnerabilities.Moreover, the concept of topologically distinct spaces extends beyond mathematics into real-world applications. In biology, the shape of proteins can determine their function, and understanding their topological features can lead to breakthroughs in drug design. Similarly, in physics, the topological properties of materials can give rise to novel states of matter, such as topological insulators, which have unique electronic properties due to their topological order.In conclusion, the term topologically encapsulates a rich and nuanced understanding of how we perceive and analyze the world around us. By focusing on properties that remain invariant under continuous transformations, we can uncover deeper truths about the nature of space, structure, and connectivity. Whether in mathematics, science, or everyday life, embracing a topological perspective opens new avenues for exploration and innovation. As we continue to investigate the topological aspects of various phenomena, we may find ourselves equipped with powerful tools to address some of the most pressing challenges in our world today.

在数学领域，特别是拓扑学中，术语topologically指的是在连续变形下保持不变的性质，如拉伸、扭曲、皱折和弯曲，但不包括撕裂或粘合。这个概念对于理解空间的本质以及不同形状如何通过不失去其基本特征而相互转化至关重要。例如，咖啡杯和甜甜圈在topologically上被认为是等价的，因为每个都可以通过一系列连续变形转变为另一个。这个想法挑战了我们对几何的传统看法，在几何中，形状通常由刚性测量和固定点定义。作为数学的一个分支，拓扑学使我们能够探索这些抽象概念，从而产生在物理学、生物学和计算机科学等多个领域的应用。当我们从topologically的角度分析物体时，我们关注的是它们的内在属性，而不是外在的测量。这种观点具有深远的意义，尤其是在理解复杂系统和现象方面。例如，在网络研究中，无论是社交网络、神经网络还是交通系统，topological结构可以揭示信息流动方式、连接方式以及系统对故障的韧性。通过从topologically的角度研究这些网络，研究人员可以识别出关键节点，如果这些节点被移除，将会破坏整个系统。这一洞察在设计更强大的网络和理解脆弱性方面是无价的。此外，topologically不同的空间概念超越了数学，进入现实世界的应用。在生物学中，蛋白质的形状可以决定其功能，理解其topological特征可以导致药物设计的突破。同样，在物理学中，材料的topological特性可以产生新型物质状态，例如拓扑绝缘体，由于其topological有序性而具有独特的电子特性。总之，术语topologically概括了我们感知和分析周围世界的丰富而细致的理解。通过关注在连续变换下保持不变的属性，我们可以揭示关于空间、结构和连通性的更深层次真理。无论是在数学、科学还是日常生活中，接受topological的视角为探索和创新开辟了新的途径。随着我们继续研究各种现象的topological方面，我们可能会发现自己拥有强大的工具来应对当今世界上一些最紧迫的挑战。