alexa The Relations between Characterized Fuzzy Proximity, Fuzzy Compact, Fuzzy Uniform Spaces and Characterized Fuzzy Ts–Spaces and Fuzzy Rk–Spaces
ISSN: 2168-9679

Journal of Applied & Computational Mathematics
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Research Article

The Relations between Characterized Fuzzy Proximity, Fuzzy Compact, Fuzzy Uniform Spaces and Characterized Fuzzy Ts–Spaces and Fuzzy Rk–Spaces

Abd-Allah AS1 and Al-Khedhairi A2*

1Department of Mathematics, College of Science, El-Mansoura University, El-Mansoura, Egypt

2Department of Statistics and Operations Research, College of Science, King Saud University, PO Box 2455, Riyadh 11451, Saudi Arabia

*Corresponding Author:
Al-Khedhairi A
Mathematics Department
College of Science and Humanity Studies
Prince Sattam Bin Abdul-Aziz University
PO Box 132012, Hotat Bani Tamim 11941, Saudi Arabia
Tel: 966 800 116 9528
E-mail: [email protected]

Received Date: December 08, 2016; Accepted Date: December 31, 2016; Published Date: January 26, 2017

Citation: Abd-Allah AS, Al-Khedhairi A (2017) The Relations between Characterized Fuzzy Proximity, Fuzzy Compact, Fuzzy Uniform Spaces and Characterized Fuzzy Ts–Spaces and Fuzzy Rk–Spaces. J Appl Computat Math 6: 337. doi: 10.4172/2168-9679.1000337

Copyright: © 2017 Abd-Allah AS, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Abstract

In this research work, we study the relations between the characterized fuzzy Ts–spaces and characterized fuzzy Rk–spaces presented in old papers, for s ∈ {0,1,2,3,3 1/2 ,4} and  k ∈ {1,2,2 1/2 ,3} and the characterized fuzzy proximity spaces presented. We also study the relations between the characterized fuzzy Ts–spaces, the characterized fuzzy Rk–spaces and the characterized fuzzy compact spaces which is presented in old paper, as a generalization of the weaker and stronger forms of the G–compactness defined by Gähler. Moreover, we show here the relations between these characterized fuzzy Ts–spaces, characterized fuzzy Rk–spaces and the characterized fuzzy uniform spaces introduced and studied by Abd-Allah in 2013 as a generalization of the weaker and stronger forms of the fuzzy uniform spaces introduced by Gähler.

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