Proximity structures and ideals

Authors

  • A. Kandil Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt Author
  • S. A. El-Sheikh Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt Author
  • M. M. Yakout Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt Author
  • Shawqi A. Hazza Department of Mathematics, Faculty of Education, Taiz University, Taiz, Yemen Author

Keywords:

ideals, basic proximity, proximity space, g-proximities, nearness, topological space

Subjects:

54E05

Abstract

In this paper, we present a new approach toproximity structures based on the recognition of many of theentities important in the theory of ideals. So, we give acharacterization of the basic proximity using ideals. Also, weintroduce the concept of $g$-proximities and we show that fordifferent choice of "$g$'' one can obtain many of the known typesof generalized proximities. Also, characterizations of some typesof these proximities – ($g_0,h_0$) – are obtained.

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Published

2015-04-15

Issue

Vol. 67 No. 2 (2015): Vol. 67, Issue 2

Section

Articles

License

Copyright (c) 2015 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.