Journal of Mathematical Sciences

, Volume 238, Issue 1, pp 32–45 | Cite as

On Semitopological Bicyclic Extensions of Linearly Ordered Groups

  • O. V. Gutik
  • K. M. Maksymyk

For a linearly ordered group G , we define a subset AG to be a shift-set if, for any x, y, z ϵ A with y < x, we get x · y-1 ··z ϵ A. We describe the natural partial order and solutions of equations on the semigroup B(A) of shifts of positive cones of A . We study topologizations of the semigroup B(A). In particular, we show that, for an arbitrary countable linearly ordered group G and a nonempty shift-set A of G , every Baire shift-continuous T1-topology τ on B(A) is discrete. We also prove that, for any linearly nondensely ordered group G and a nonempty shift-set A of G , every shift-continuous Hausdorff topology τ on the semigroup B (A) is discrete.


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Authors and Affiliations

  • O. V. Gutik
    • 1
  • K. M. Maksymyk
    • 1
  1. 1.I. Franko Lviv National UniversityLvivUkraine

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