Affiliations: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China | School of Science, Mudanjiang Normal University, Mudanjiang, P.R. China | School of Science, University of Science and Technology Liaoning, P.R. China
Note: [] Corresponding author. Bing Wang, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China. E-mail: [email protected]
Note: [] Corresponding author. Guiyang Ding, School of Science, University of Science and Technology Liaoning, Liaoning 114051, P.R. China. E-mail: [email protected]
Abstract: In this paper, a completion theorem for gradual metric space and a completion theorem for gradual normed linear space are proved. The completion spaces are defined by means of an equivalence relation obtained by convergence of sequences via the gradual metrics and the gradual norms, respectively.
