Affiliations: Institute of Mathematics, School of Mathematics Sciences, Nanjing Normal University, Nanjing Jiangsu, People’s Republic of China
Correspondence:
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Corresponding author. Cong-hua Yan, Institute of Mathematics, School of Mathematics Sciences, Nanjing Normal University, Nanjing Jiangsu 210023, People’s Republic of China. Tel: +8602585481541; Fax: +8602583598493; E-mail: rshalaby@nu.edu.eg.
Note: [1] Project Supported by the National Natural Science Foundation of China (Grant No.: 11571006 and No.: 12071225) and by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).
Abstract: Motivated by the concept of lattice-bornological vector spaces of J. Paseka, S. Solovyov and M. Stehlík, which extends bornological vector spaces to the fuzzy setting over a complete lattice, this paper continues to study the theory of L-bornological vector spaces. The specific description of L-bornological vector spaces is presented, some properties of Lowen functors between the category of bornological vector spaces and the category of L-bornological vector spaces are discussed. In addition, the notions and some properties of L-Mackey convergence and separation in L-bornological vector spaces are showed. The equivalent characterization of separation in L-bornological vector spaces in terms of L-Mackey convergence is obtained in particular.
Keywords: L-bornological vector spaces, L-Mackey convergence, Separation, The product L-bornological vector spaces, The quotient L-bornological vector spaces
