T-proximity compatible with T-neighbourhood structure | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 20, Issue 2, 2012, Pages 108-115 PDF (344.93 K) | ||
| DOI: org/10.1016/j.joems.2012.08.004 | ||
| Author | ||
| Khaled A. Hashem | ||
| Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt | ||
| Abstract | ||
| In this paper, we show that every T-neighbourhood space induces a T-proximity space, where T stands for any continuous triangular norm. An axiom of T-completely regular of T-neighbourhood spaces introduced by Hashem and Morsi (2003) [3], guided by that axiom we supply a Sierpinski object for category T-PS of T-proximity spaces. Also, we define the degree of functional T-separatedness for a pair of crisp fuzzy subsets of a T-neighbourhood space. Moreover, we define the Cˇ ech T-proximity space of a T-completely regular T-neighbourhood space, hence, we establishes it is the finest T-proximity space which induces the given T-neighbourhood space. | ||
| Keywords | ||
| Triangular norm; T-neighbourhood spaces; T-proximity spaces | ||
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