Discussiones Mathematicae General Algebra and Applications 24(2) (2004)
211-223
DOI: https://doi.org/10.7151/dmgaa.1086
CONVERGENCE WITH A REGULATOR IN DIRECTED GROUPS
Stefan Cernak
>Department of Mathematics,
Faculty of Civil Engineering, Technical University,
Vysokoskolska 4, SK-042 02 Kosice,
Slovakia
and/or
Mathematical Institute, Slovak Akademy of Sciences
Gresakova 6, SK-04001 Kosice, Slovakia
e-mail: Stefan.Cernak@tuke.sk
Abstract
There is defined and studied a convergence with a fixed regulator u in directed groups. A u-Cauchy completion of an integrally closed directed group is constructed.Keywords: convergent sequence, fundamental sequence, Cauchy completion, integrally closed directed group, convergence regulator, vector lattice.
2000 Mathematics Subject Classification: 06F15, 20F60.
References
[1] | S. Cernak and J. Lihova, Convergence with a regulator in lattice ordered groups, Tatra Mt. Math. Publ. to appear. |
[2] | M.R. Darnel, Theory of Lattice-Ordered Groups, M. Dekker, Inc., New York 1995 |
[3] | L. Fuchs, Partially Ordered Algebraic Systems, Pergamon Press., Oxford 1963. |
[4] | A.M.W. Glass, Partially Ordered Groups, World Scientific Publ. Co., River Edge, NJ, 1999. |
[5] | W.A.J. Luxemburg and A. C. Zaanen, Riesz Spaces, vol. I, North-Holland, Amsterdam-London 1971. |
[6] | B.Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces, Wolters-Noordhoff Sci. Publ., Groningen 1967 (The original Russian edition in: Fizmatgiz, Moskow 1961). |
Received 14 April 2004
Revised 27 December 2004
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