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ArticleOriginal scientific text

Title

Convergence with a regulator in directed groups

Authors 1, 2

Affiliations

  1. Department of Mathematics, Faculty of Civil Engineering, Technical University, Vysokoškolská 4, SK-042 02 Košice, Slovakia
  2. Mathematical Institute, Slovak Akademy of Sciences, Grešaková 6, SK-04001 Košice, Slovakia

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

ENG
convergent sequence, fundamental sequence, Cauchy completion, integrally closed directed group, convergence regulator, vector lattice

Bibliography

  1. S. Černák 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).
Discussiones Mathematicae - General Algebra and Applications
2004/24/2
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Pages:
211-223
Main language of publication
English
Received
2004-04-14
Accepted
2004-12-27
Published
2004

DOI: 10.7151/dmgaa.1086

Exact and natural sciences