Abstract

In this paper, we present a new approach to proximity structures based on the recognition of many of the entities important in the theory of ideals. So, we give a characterization of the basic proximity using ideals. Also, we introduce the concept of $g$-proximities and we show that for different choice of ``$g$'' one can obtain many of the known types of generalized proximities. Also, characterizations of some types of these proximities -- ($g_0,h_0$) -- are obtained.

Keywords: ideals; basic proximity; proximity space; g-proximities; nearness; topological space.

MSC: 54E05

Pages:  130$-$142     

Volume  67 ,  Issue  2 ,  2015