On compactness and paracompactness in interval-valued metric spaces

Computer Engineering and Applications ›› 2013, Vol. 49 ›› Issue (23): 45-47.

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On compactness and paracompactness in interval-valued metric spaces

CHEN Guixiu1，2, LI Shenggang1，ZHAO Hu1

1.College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
2.Department of Mathematics, Qinghai Normal University, Xining 810008, China

Online:2013-12-01 Published:2016-06-12

区间值度量空间的紧性和仿紧性

陈桂秀1，2，李生刚1，赵虎1

1.陕西师范大学数学与信息科学学院，西安 710062
2.青海师范大学数学系，西宁 810008

Abstract

Abstract: The definition of interval-valued metric spaces is introduced, according to the definition of compactness and their related equivalent relations in general topological spaces, the compactness and a set of equivalent relations of induced topological space by interval-valued metric are proved, the paracompactness of this induced topological space is discussed in the paper.

Key words: interval number, interval-valued metric space, compactness, paracompactness

摘要： 给出了区间值度量空间的概念，根据一般拓扑学中紧性的相关定义及其等价条件，证明了由区间值度量诱导的拓扑具有的紧性及其一系列等价关系，讨论了该诱导的拓扑空间具有仿紧性。

关键词: 区间数, 区间值度量空间, 紧性, 仿紧性

CHEN Guixiu1，2, LI Shenggang1，ZHAO Hu1. On compactness and paracompactness in interval-valued metric spaces[J]. Computer Engineering and Applications, 2013, 49(23): 45-47.

陈桂秀1，2，李生刚1，赵虎1. 区间值度量空间的紧性和仿紧性[J]. 计算机工程与应用, 2013, 49(23): 45-47.

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On compactness and paracompactness in interval-valued metric spaces

区间值度量空间的紧性和仿紧性

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