On the lattice of weak topologies on the bicyclic monoid with adjoined zero
A Hausdorff topology τ on the bicyclic monoid with adjoined zero C⁰ is called weak if it is contained in the coarsest inverse semigroup topology on C⁰. We show that the lattice W of all weak shift-continuous topologies on C⁰ is isomorphic to the lattice SIF¹×SIF¹ where SIF¹ is the set of all shift-...
Збережено в:
| Дата: | 2020 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2020
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/188551 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the lattice of weak topologies on the bicyclic monoid with adjoined zero / S. Bardyla, O. Gutik // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 26–43. — Бібліогр.: 30 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | A Hausdorff topology τ on the bicyclic monoid with adjoined zero C⁰ is called weak if it is contained in the coarsest inverse semigroup topology on C⁰. We show that the lattice W of all weak shift-continuous topologies on C⁰ is isomorphic to the lattice SIF¹×SIF¹ where SIF¹ is the set of all shift-invariant filters on ! with an attached element 1 endowed with the following partial order: F ≤ G if and only if G = 1 or F ⊂ G. Also, we investigate cardinal characteristics of the lattice W. In particular, we prove that W contains an antichain of cardinality 2ᶜ and a well-ordered chain of cardinality c. Moreover, there exists a well-ordered chain of first-countable weak topologies of order type t. |
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