Word · Frequency #29554
topologies
拓扑学
topologies is the plural of topology.
the branch of mathematics that studies properties of geometric figures which remain unchanged under continuous deformations, such as stretching or bending.
- 1.
The branch of mathematics dealing with those properties of a geometrical object (of arbitrary dimensionality) that are unchanged by continuous deformations (such as stretching, bending, etc., without tearing or gluing).
数学分支,研究几何对象在连续变形下保持不变的性质。
- 2.
Any collection τ of subsets of a given set X that contains both the empty set and X, and which is closed under finitary intersections and arbitrary unions.
给定集合X的子集族,包含空集和X,并对有限交集和任意并集封闭。
- 3.
The anatomical structure of part of the body.
身体某部分的解剖结构。
- 4.
The arrangement of nodes in a communications network.
通信网络中节点的排列方式。
- 5.
The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.
特定技术实现中不受物理布局或应用形式差异影响的特性。
- 6.
The topographical study of geographic locations or given places in relation to their history.
对地理位置或特定地方及其历史的地形学研究。
地志学；数学分支,研究几何对象在连续变形下保持不变的性质。；给定集合X的子集族,包含空集和X,并对有限交集和任意并集封闭。；身体某部分的解剖结构。；通信网络中节点的排列方式。
In use
In topology, a doughnut and a coffee cup are considered the same because they both have one hole.
Our professor introduced topology as the study of properties that remain unchanged when an object is stretched, bent, or twisted.
For her project, she explored how topology helps mathematicians understand the structure of space beyond ordinary measurements.
Connections
Word family
- topologies
- plural
Learner notes
Grammar Note
作“拓扑学/地志学”等学科、领域讲时通常不可数；指某个集合或网络的具体拓扑结构时可数，复数为 topologies。
Learn the forms together
页面下方列出了常见词形变化。学习时注意它们在句子中的语法位置。
Dictionary facts from ECDICT, WIKTIONARY.