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Completion of cone metric spaces. (English) Zbl 1195.54057

Summary: In this paper a completion theorem for cone metric spaces and a completion theorem for cone normed spaces are proved. The completion spaces are defined by means of an equivalence relation obtained by convergence via the scalar norm of the Banach space \(E\).

MSC:

54E50 Complete metric spaces
46B99 Normed linear spaces and Banach spaces; Banach lattices
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
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