contractible

contractible 的音标是[kənˈtræktəbl]，基本翻译是可缩小的、可缩拢的。

速记技巧：将单词拆分记忆，可以分成con-tract-ible三个部分，其中con表示“共同”，tract表示“拉；割”，ible表示“能够的，可能的”因此整体记忆，con和tract在一起就是“共同收缩”的意思，可以理解为可缩小的。

contractible 的英文词源为：contract（收缩）+ -ible（可…的）。

变化形式：可变化形式为 contractible 和 contractibility。

相关单词：

1. contract（收缩）：该词本身有形容词形式contractive，表示与收缩相关的含义。

2. contraction（收缩）：表示物体或组织收缩的现象。

3. contractile（可收缩的）：该词表示可以收缩的，与contractible意思相近。

4. expansibility（可扩张性）：表示物体或组织可以扩张或伸展的性质，与contractibility意思相反。

5. extensible（可伸展的）：表示可以伸展或延长的，与contractibility和extensibility意思相近。

6. extendibility（可扩展性）：表示物体或组织可以扩展或延伸的性质，与contractibility和extensibility意思相反。

7. distensible（可膨胀的）：表示可以膨胀的，与contractibility和distension意思相近。

8. distension（膨胀）：表示物体或组织膨胀的现象，与distensible相关联。

9. collapsible（可折叠的）：表示可以折叠或弯曲的物体或结构，与contractibility和collapsible意思相近。

10. foldable（可折叠的）：表示可以折叠的物体或材料，与contractibility和folding意思相近。

常用短语：

1. contractible with

2. contractibility condition

3. contractible spaces

4. contractibility radius

5. contractible sets

6. contractible under

7. contractible to

双语例句：

1. The manifold is contractible with the circle.

这个流形与圆相交时是可缩的。

2. The contractibility condition is a necessary and sufficient condition for the existence of solutions to certain differential equations.

可缩性条件是某些微分方程存在解的必要且充分条件。

3. Contractible spaces are often diffeomorphic to Euclidean spaces.

可缩空间通常与欧几里得空间同胚。

4. The contractibility radius of a manifold depends on its dimension and topology.

流形的可缩半径取决于它的维数和拓扑性质。

5. The set of points that are contractible to a point is called the point-set topology.

可缩到一点的点的集合被称为点集拓扑。

6. Under the mapping, the domain is contractible to the image.

在映射下，域被可缩到像。

7. The question of whether two manifolds are contractible to each other is a subtle one.

两个流形是否可以彼此可缩的问题是一个微妙的问题。

英文小作文：

Contractibility is a fundamental concept in topology that deals with the possibility of a space being shrunk to a smaller space under certain conditions. In this context, contractibility plays an important role in determining the topological properties of a space.

For instance, contractibility can be used to determine whether a space is simply connected or not. If a space is contractible to a point, then it is simply connected, which means that it cannot support any non-trivial continuous field or connection. This property is crucial for understanding the topology of certain systems, such as quantum fields and strings, which are often described using topological concepts like contractibility and homology.

In practice, contractibility is often used in the study of manifolds, which are mathematical objects that can be thought of as generalizations of three-dimensional space. Understanding the contractibility of manifolds is crucial for understanding their topology and geometry, and can lead to new insights into their mathematical and physical properties.

In conclusion, contractibility is a fundamental concept in topology that plays an important role in understanding the topological properties of spaces and manifolds. Understanding its implications and applications can lead to new insights into various systems and fields of mathematics and physics.