DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

PDF

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


Close