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Positivity

, Volume 23, Issue 4, pp 811–827 | Cite as

On the topological mass lattice groups

  • M. PourgholamhosseinEmail author
  • M. A. Ranjbar
Article
First Online:
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Abstract

Let G to be a torsion free abelian group. In this paper we introduce the following concepts:
  1. (1)

    Algebraic line, algebraic line segment and thin convex subsets of G.

     
  2. (2)

    Absorbing topological group, that is a generalization of topological vector space.

     
  3. (3)

    A special subset of a mass lattice group (G, \(\le \)) called a link in G which we can construct a locally solid topology on G by it.

     
Some interesting results about unital lattice groups and Riesz spaces with the chief link topology on them have been presented.

Keywords

Lattice group Mass group Locally solid topology Retraction Link Absorbing topological group 

Mathematics Subject Classification

Primary: 22A10 06F20 46A40 57N17 Secondary: 54H12 22A26 54F05 
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Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesUniversity of QomQomIran

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