Completion of Vector Metric Spaces

Cüneyt Çevik
2.290 529


In this study a completion theorem for vector metric spaces is proved. The completion spaces are defined by means of an equivalence relation obtained by order convergence via the module of the Riesz space E.


Vector metric space, order-Cauchy sequence, order-Cauchy completion, Riesz space, Banach lattice

Full Text:



C. D. Aliprantis, K. C. Border, Infinite Dimensional Analysis, Springer-Verlag, Berlin, 1999.

I. Altun, C. Çevik, Some common fixed point theorems in vector metric spaces, Filomat, 25(1), (2011), 105-113.

C. Çevik, I. Altun, Vector metric spaces and some properties, Topol. Methods Nonlinear Anal., 34(2) (2009), 375-382.

C. Çevik, On continuity of functions between vector metric spaces, J. Funct. Spaces, (2014) Article ID 753969, 6 pages.

F. Dashiell, A. Hager, M. Henriksen, Order-Cauchy completions of rings and vector lattices of continuous functions, Can. J. Math. (3) 32 (1980), 657-685.

C. J. Everett, Sequence completion of lattice moduls, Duke Math. J. 11 (1944), 109-119.

J.L. Krivine, Theoremes de factorisation dans les espaces reticules, Seminaire Maurey-Schwartz (1973- 74), Exposes 22-23, École Polytechnique, Paris.

Y. Lindenstrauss, L. Tzafriri, Classical Banach Spaces II, Springer-Verlag, Berlin-Heidelberg-New York, 1979.

W. A. J. Luxemburg, A. C. Zaanen, Riesz Space I, North-Holland, Amsterdam, 1971.

Zs. Páles, I.-R. Petre, Iterative fixed point theorems in E-metric spaces, Acta Math. Hungar., 140(1-2), (2013) 134-144.

F. Papangelou, Order convergence and topological completion of commutative lattice-groups, Math. Annalen 155 (1964), 81-107.

I.-R. Petre, Fixed point theorems in vector metric spaces for single-valued operators, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity, 9 (2011), 59-80.

I.-R. Petre, Fixed points for ϕ-contractions in E- Banach spaces, Fixed Point Theory, 13(2), (2012), 623- 640.

V. Zaharov, On functions connected with sequential absolute, Cantor completions and classical rings of quotients, Periodica Math. Hungar. 19 (1988), 113-133.