Open AccessT-proximity compatible with T-neighbourhood structure
Author(s) -
Khaled A. Hashem
Publication year - 2012
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2012.08.004
Subject(s) - neighbourhood (mathematics) , mathematics , axiom , sierpinski triangle , space (punctuation) , combinatorics , discrete mathematics , computer science , mathematical analysis , geometry , fractal , operating system
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 Čech 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