Affiliations: Beijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China
Correspondence:
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Corresponding author. Xiao-Wu Zhou, Beijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, P.R. China. E-mail: zhouxiaowu901@163.com.
Abstract: Considering L be a completely distributive lattice, the notion of the sum of L-convex spaces is introduced and its elementary properties is studied. Firstly, the connections between the sum of L-convex spaces and its factor spaces are established. Secondly, the additivity of separability (S-1, sub-S0, S0, S1, S2, S3 and S4) are investigated. Finally, the additivity of five types special L-convex spaces are examined.
Keywords: L-convex space, sum of L-convex space, separability, additivity
