On Semitopological Bicyclic Extensions of Linearly Ordered Groups
- 作者: Gutik O.1, Maksymyk K.1
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隶属关系:
- I. Franko Lviv National University
- 期: 卷 238, 编号 1 (2019)
- 页面: 32-45
- 栏目: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242476
- DOI: https://doi.org/10.1007/s10958-019-04216-x
- ID: 242476
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详细
For a linearly ordered group G , we define a subset A ⊆ G 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.
作者简介
O. Gutik
I. Franko Lviv National University
Email: Jade.Santos@springer.com
乌克兰, Lviv
K. Maksymyk
I. Franko Lviv National University
Email: Jade.Santos@springer.com
乌克兰, Lviv