逼近空间的拓扑方法

Topological Approach for Proximity Spaces

逼近空间理论最早由V.A.Efremovi教授于1952年从拓扑角度建立起来,最近,Dimiter Vakarelov和Ivo Duntsch等应用该理论于空间推理.本文从格及拓扑角度来研究逼近空间的若干性质,研究了弱逼近空间以及其与正则开集簇的联系,同时研究了逼近空间的和,给出了从一簇逼近空间来构造和空间的一般方法.最后给出了构造严格(弱)预逼近空间的一种方法.

The theory of proximity spaces was found early in 1952 by professor V. A. Efremovie from topological point of view. Recently Dimiter Vakarelov and Ivo Duntsch etc. applied this theory to the field of QSR. In this paper, we mainly investigate some properties of proximity spaces from lattice and topological point of view. This paper investigate weak proximity space and it＇ s relationship with regular open sets, meanwhile this paper investigated the sum of proximity space, we give a general method of constructing sum space from a family of proximity spaces. At last, we propose a method of constructing of strict（weak） pre - proximity space.