“open set”的概念、定义、习题解题方法及翻译-数学辞典

单词

open set

释义

open set

A subset A of a metric space M is open if every point of A is an interior point of A or, equivalently, around each point of A there exists an open ball of M which is contained in A. The open sets form the topology of M. In a topological space the open sets are, by definition, those sets in the topology.

Note that openness is a relative term and that open sets are open in another set. So [0,1) is not open in R as 0 is not an interior point but [0,1) is open in [0,∞). See clopen set, closed set.

随便看

数学辞典收录了4151条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。