topology

Topology

Topology 是一个名词，主要用于数学和计算机科学领域，指的是空间的结构和性质。它也可以用作形容词，描述与这些结构和性质相关的事物。

词汇分析

• Topology as a noun refers to the study of geometric properties and spatial relations unaffected by the continuous change of shape or size of figures.

  拓扑作为名词指的是研究几何属性和空间关系，这些属性和关系不受图形形状或大小连续变化的影响。

• Topological as an adjective describes something that is related to topology.

  拓扑的作为形容词，描述与拓扑相关的事物。

词语辨析

• In mathematics, topology is crucial for understanding the properties of space.

  在数学中，拓扑对理解空间的属性至关重要。

• The topological properties of a shape do not change even if it is stretched.

  一个形状的拓扑特性即使被拉伸也不会改变。

近义词

• Geometry (几何学)
• Topology (拓扑学)
• Spatial relations (空间关系)

反义词

• Disorder (无序)
• Chaos (混沌)

柯林斯词典

According to Collins Dictionary, topology refers to the branch of mathematics that deals with the properties of space that are preserved under continuous transformations.

根据柯林斯词典，拓扑学是研究在连续变换下保留的空间属性的数学分支。

牛津词典

The Oxford Dictionary defines topology as the study of geometric properties and spatial relations unaffected by the continuous change of shape or size of figures.

牛津词典将拓扑学定义为研究在形状或大小的连续变化中不受影响的几何属性和空间关系。

用法

• The study of topology is essential for advanced mathematics.

  对拓扑的研究对高级数学而言是必不可少的。

• Understanding topological spaces can help solve complex problems.

  理解拓扑空间可以帮助解决复杂问题。

例句

• In algebraic topology, we study shapes through their properties.

  在代数拓扑中，我们通过形状的属性来研究它们。

• The topological structure of the network is important for its efficiency.

  网络的拓扑结构对其效率至关重要。

• Different topologies can lead to different behaviors in systems.

  不同的拓扑可以导致系统中出现不同的行为。

• The topological classification of surfaces is a fundamental concept in math.

  表面的拓扑分类是数学中的一个基本概念。

• In computer science, topological data analysis is a growing field.

  在计算机科学中，拓扑数据分析是一个快速发展的领域。

• Topology can help in understanding the connectivity of data.

  拓扑学有助于理解数据的连接性。

• The topological changes in the material affect its properties.

  材料中的拓扑变化会影响其属性。

• He presented a paper on topological spaces in his seminar.

  他在研讨会上发表了一篇关于拓扑空间的论文。

• The topology of the brain's neural networks is still being studied.

  大脑神经网络的拓扑仍在研究中。

• Mathematicians often use topological methods to solve problems.

  数学家们常常使用拓扑方法来解决问题。

• Understanding topology is crucial for studying advanced physics.

  理解拓扑对研究高级物理至关重要。

• The concept of topological equivalence is fundamental in mathematics.

  拓扑等价的概念在数学中是基础的。

• We examined the topological features of the data set.

  我们检查了数据集的拓扑特征。

• Topology plays a vital role in understanding continuity.

  拓扑学在理解连续性中发挥着重要作用。

• The topological analysis provided insights into the data.

  这种拓扑分析为数据提供了洞察。

• His research focused on topological data analysis methods.

  他的研究集中在拓扑数据分析方法上。

• She is studying the topology of complex systems.

  她正在研究复杂系统的拓扑。

• Topological defects can affect the properties of materials.

  拓扑缺陷会影响材料的性质。

• The topological properties of the material were analyzed.

  该材料的拓扑特性得到了分析。