MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Proximity structures and ideals
A. Kandil, S. A. El-Sheikh, M. M. Yakout and Shawqi A. Hazza

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.

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

MSC: 54E05

Pages:  130--142     

Volume  67 ,  Issue  2 ,  2015