homeomorphic

简明释义

英[/ˌhoʊmiəˈmɔrfɪk/]美[/ˌhoʊmiəˈmɔrfɪk/]

adj. 同胚的

英英释义

单词用法

同义词

反义词

例句

1.We give a sufficient condition for the self-similar set in the plane which is homeomorphic to the unit disk.

最后一章讨论自相似集的拓扑结构，给出了平面上的自相似集同胚于单位圆盘的充分条件。

2.As mathematicians say, “Every simply connected closed 3-manifold is homeomorphic to a 3-sphere.”

用数学语言表达就是“每个单连通3重（3-manifold）封闭体与一个三维球体同胚（homeomorphic）。”

3.This paper tries to define metric function for homeomorphic mapping, and a sufficient condition of bounded metric function is given, under which a upper bound of metric function is defined as well.

对于一个同胚映射，本文给出了度量函数的定义，并且给出了度量函数有界的一个充分条件及在此充分条件下度量函数的一个上界。

4.In this paper, some results on fixed points of homeomorphic maps in metric Spaces have been obtained.

本文给出了度量空间中某些同胚非扩张映射不动点存在的充分必要条件。

5.The method was based on a homeomorphic transformation of the infinity into the origin(linear singular point).

用一同胚变换将无穷远点转变成原点（初等奇点）。

6.As mathematicians say, "Every simply connected closed 3-manifold is homeomorphic to a 3-sphere."

用数学语言表达就是“每个单连通3重（3-manifold）封闭体与一个三维球体同胚（homeomorphic）。”

7.It is proved that relative hereditary, relative closed transition, weak homeomorphic invariant, L-good extension are all valid.

证明了相对正规分离性是遗传的、相对闭集传递的、弱同胚不变的、L -好的推广性质。

8.Results Generalizing some results of homeomorphic morphism, homotopy equivalence and homotopy regular morphism.

结果推广了同胚映射、同伦等价和同伦正则态射的有关结果。

9.This paper tries to define metric function for homeomorphic mapping, and a sufficient condition of bounded metric function is given, under which a upper bound of metric function is defined as well.

对于一个同胚映射，本文给出了度量函数的定义，并且给出了度量函数有界的一个充分条件及在此充分条件下度量函数的一个上界。

10.In algebraic topology, we explore homeomorphic relationships between various geometric figures.

在代数拓扑中，我们探索各种几何图形之间的同胚关系。

11.Mathematicians often study homeomorphic spaces to understand their properties.

数学家们经常研究同胚空间以理解它们的性质。

12.In topology, two shapes are considered homeomorphic if they can be transformed into each other without cutting or gluing.

在拓扑学中，如果两个形状可以在不切割或粘合的情况下相互转换，则它们被认为是同胚的。

13.The donut and the coffee cup are homeomorphic because one can be deformed into the other.

甜甜圈和咖啡杯是同胚的，因为一个可以变形为另一个。

14.A sphere and a cube are not homeomorphic due to their different topological properties.

球体和立方体不是同胚的，因为它们具有不同的拓扑性质。

作文

In the realm of mathematics, particularly in topology, the concept of homeomorphic plays a crucial role in understanding the properties of spaces. A space is considered homeomorphic to another if there exists a continuous, bijective function between them that has a continuous inverse. This definition might sound complex, but it essentially means that two spaces can be transformed into each other without tearing or gluing. This characteristic allows mathematicians to classify shapes and spaces based on their intrinsic properties rather than their superficial appearances.To illustrate the idea of homeomorphic spaces, consider a simple example: a coffee cup and a doughnut (torus). At first glance, these two objects seem entirely different; one is used for drinking while the other is a popular baked good. However, if we think in terms of topology, we can visualize how a coffee cup can be deformed into a doughnut shape by stretching and bending without cutting or gluing. The handle of the cup corresponds to the hole in the doughnut, making these two objects homeomorphic.This concept extends beyond simple examples. In higher dimensions, we can find more complex homeomorphic relationships. For instance, a sphere and an ellipsoid are homeomorphic because we can continuously deform one into the other. Such transformations are vital for topologists, as they help classify surfaces and understand their properties in a more profound way.The significance of homeomorphic spaces can also be appreciated in various fields such as physics and computer science. In physics, understanding the homeomorphic nature of different states of matter can lead to insights into phase transitions. Similarly, in computer graphics, homeomorphic mappings are essential for rendering shapes and surfaces accurately, allowing for realistic animations and simulations.Moreover, the study of homeomorphic spaces encourages abstract thinking. It challenges us to look beyond the physical attributes of objects and consider their underlying structures. This mindset can be beneficial not only in mathematics but also in everyday problem-solving. For instance, when faced with a complex issue, thinking about how different components might relate to one another through homeomorphic transformations can lead to innovative solutions.In conclusion, the term homeomorphic embodies a profound concept in topology that transcends mere geometric shapes. Its implications stretch into various disciplines, encouraging a deeper understanding of continuity and transformation. By recognizing that seemingly disparate objects can share fundamental properties, we gain a richer perspective on the world around us. Embracing the idea of homeomorphic relationships not only enhances our mathematical knowledge but also fosters creativity and innovation in diverse fields.

在数学领域，特别是拓扑学中，homeomorphic的概念在理解空间属性方面起着至关重要的作用。如果两个空间之间存在一个连续的双射函数，并且这个函数有一个连续的逆，那么这两个空间就被认为是homeomorphic的。这个定义听起来可能很复杂，但它本质上意味着两个空间可以在不撕裂或粘合的情况下相互转化。这一特性使得数学家能够根据空间的内在属性而不是表面外观对形状和空间进行分类。为了说明homeomorphic空间的概念，我们可以考虑一个简单的例子：咖啡杯和甜甜圈（环面）。乍一看，这两个物体似乎完全不同；一个用于饮水，而另一个是受欢迎的烘焙食品。然而，如果我们从拓扑的角度思考，我们可以想象如何通过拉伸和弯曲将咖啡杯变形成甜甜圈的形状，而不需要切割或粘合。杯子的把手对应于甜甜圈的孔，使这两个物体成为homeomorphic的。这一概念超越了简单的例子。在更高维度中，我们可以发现更复杂的homeomorphic关系。例如，一个球体和一个椭球体是homeomorphic的，因为我们可以将一个连续变形为另一个。这种变换对拓扑学家来说至关重要，因为它们帮助分类表面并以更深刻的方式理解其性质。homeomorphic空间的重要性在物理学和计算机科学等多个领域也得到了认可。在物理学中，理解不同物态的homeomorphic特性可以为相变提供洞察。同样，在计算机图形学中，homeomorphic映射对于准确渲染形状和表面至关重要，从而实现逼真的动画和模拟。此外，研究homeomorphic空间鼓励抽象思维。它挑战我们超越物体的物理属性，考虑它们的基本结构。这种思维方式不仅在数学中是有益的，而且在日常问题解决中也是如此。例如，当面临复杂问题时，考虑不同组件如何通过homeomorphic变换相互关联，可以带来创新的解决方案。总之，homeomorphic一词体现了拓扑学中的一个深刻概念，它超越了单纯的几何形状。它的影响延伸到各个学科，鼓励人们对连续性和变换有更深刻的理解。通过认识到看似不相关的物体可以共享基本属性，我们对周围世界有了更丰富的视角。接受homeomorphic关系的想法不仅增强了我们的数学知识，还促进了各个领域的创造力和创新。