Affiliations: [a] School of Math. Sciences, Suzhou University of Science and Technology, Suzhou, Jiangsu, China
| [b] Institute of Math., School of Math. Sciences, Nanjing Normal University, Nanjing Jiangsu, People’s Republic of China
Correspondence:
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Corresponding author. Cong-Hua Yan, Institute of Math., School of Math. Sciences, Nanjing Normal University, Nanjing Jiangsu 210023, People’s Republic of China. E-mail: chyan@njnu.edu.cn.
Abstract: In this paper, a notion of fuzzifying bornological linear spaces is introduced and the necessary and sufficient condition for fuzzifying bornologies to be compatible with linear structure is discussed. The characterizations of convergence and separation in fuzzifying bornological linear spaces are showed. In particular, some examples with respect to linear fuzzifying bornologies induced by probabilistic normed spaces and fuzzifying topological linear spaces are also provided.
Keywords: Fuzzifying bornological linear spaces, fuzzifying bornological convergence, separation, Product linear fuzzifying bornologies, quotient linear fuzzifying bornologies
