Discussion About the Property of Metric Spaces

Abstract

In every branch of mathematics, such as mathematics analysis, real variable function theory, the theory of functional analysis, etc., the concept of distance is often used, the one in it can define the distance of space and the one can be called a distance space, sometimes, even in mathematics itself other than in the natural sciences, also often use tools or some results of the distance space, in this article, we defines some distance in real space, and the sequence limit, limit of Cauchy sequences and so on, to do a thorough research the distance and distance space, finally we obtained some important properties in the space.