In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. [1] Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry.

度量空间（metric space）是一种具有 度量函数 （metric function）或者叫做 距离函数 （distance function）的集合，此函数定义集合内所有元素间的距离，被称为集合上的metric。 度量空间中最符合直观理解的是 三维欧氏空间 ，事实上，metric的概念是 欧氏距离 性质的推广。

在数学中，距离函数（distance function）或度量（度規）函数（metric function）是個函數，定义了集合內每一對元素之间的距离。带有度量的集合叫做度量空间。度量能導出集合上的拓扑，但不是所有拓扑都可以由度量生成。

度量（metric），亦称距离函数，数学概念，是度量空间中满足特定条件的特殊函数，一般用d表示。 度量空间也叫做距离空间，是一类特殊的拓扑空间。

2025年1月10日 · A metric satisfies the triangle inequality g(x,y)+g(y,z)>=g(x,z) (1) and is symmetric, so g(x,y)=g(y,x). (2) A metric also satisfies g(x,x)=0, (3) as well as the condition that g(x,y)=0 implies x=y.

拓扑学是研究几何图形或空间在连续改变形状后还能保持不变的一些性质的学科,它只考虑物体间的位置关系而不考虑它们的形状和大小 （百度百科）。 简而言之，它是研究空间所包含的性质的数学分支。 换句话说，在某个空间里，物体之间的位置关系始终遵循某些固定的规则，而这些规则是这个空间本身赋予的，和放进这个空间内的物体并没有关系。 因此拓扑学里有一个最基本的概念便是 “拓扑空间”，而拓扑空间的本质便是集合，且这个集合内的元素（不仅仅是单个的点，还包 …

在数学中，距离函数（distance function）或度量（度规）函数（metric function）是个函数，定义了集合内每一对元素之间的距离。带有度量的集合叫做度量空间。度量能导出集合上的拓扑，但不是所有拓扑都可以由度量生成。

A metric space is a set X that has a notion of the distance d(x, y) between every pair of points x, y X. The purpose of this chapter is to introduce metric spaces and give some definitions and examples. We do not develop their theory in detail, and …

2021年10月29日 · In mathematics, a metric or distance function is a function that gives a distance between each pair of point elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set, but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is called metrizable.

Then we call (M;d) a metric space, and the function da metric. A metric formalizes the idea of the distance between points in a set. The rst two conditions are easy to justify conceptually: distance cannot be negative, can only be zero between two identical points, and does not depend upon the order in which you consider points.