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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