On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point
In this paper we study the semigroup IC(I,[a]) (IO(I,[a])) of closed (open) connected partial homeomorphisms of the unit interval I with a fixed point a∈I. We describe left and right ideals of IC(I,[0]) and the Green's relations on IC(I,[0]). We show that the semigroup IC(I,[0]) is bisimple and...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2011 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/154866 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point / I. Chuchman // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 2. — С. 38–52. — Бібліогр.: 10 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-154866 |
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Chuchman, I. 2019-06-16T05:51:42Z 2019-06-16T05:51:42Z 2011 On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point / I. Chuchman // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 2. — С. 38–52. — Бібліогр.: 10 назв. — англ. 1726-3255 2010 Mathematics Subject Classification:20M20,54H15, 20M18. https://nasplib.isofts.kiev.ua/handle/123456789/154866 In this paper we study the semigroup IC(I,[a]) (IO(I,[a])) of closed (open) connected partial homeomorphisms of the unit interval I with a fixed point a∈I. We describe left and right ideals of IC(I,[0]) and the Green's relations on IC(I,[0]). We show that the semigroup IC(I,[0]) is bisimple and every non-trivial congruence on IC(I,[0]) is a group congruence. Also we prove that the semigroup IC(I,[0]) is isomorphic to the semigroup IO(I,[0]) and describe the structure of a semigroup II(I,[0])=IC(I,[0])⊔IO(I,[0]). As a corollary we get structures of semigroups IC(I,[a]) and IO(I,[a]) for an interior point a∈I. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point |
| spellingShingle |
On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point Chuchman, I. |
| title_short |
On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point |
| title_full |
On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point |
| title_fullStr |
On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point |
| title_full_unstemmed |
On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point |
| title_sort |
on a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point |
| author |
Chuchman, I. |
| author_facet |
Chuchman, I. |
| publishDate |
2011 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
In this paper we study the semigroup IC(I,[a]) (IO(I,[a])) of closed (open) connected partial homeomorphisms of the unit interval I with a fixed point a∈I. We describe left and right ideals of IC(I,[0]) and the Green's relations on IC(I,[0]). We show that the semigroup IC(I,[0]) is bisimple and every non-trivial congruence on IC(I,[0]) is a group congruence. Also we prove that the semigroup IC(I,[0]) is isomorphic to the semigroup IO(I,[0]) and describe the structure of a semigroup II(I,[0])=IC(I,[0])⊔IO(I,[0]). As a corollary we get structures of semigroups IC(I,[a]) and IO(I,[a]) for an interior point a∈I.
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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/154866 |
| citation_txt |
On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point / I. Chuchman // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 2. — С. 38–52. — Бібліогр.: 10 назв. — англ. |
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