On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point
In this paper we study the semigroup \(\mathfrak{IC}(I,[a])\) (\(\mathfrak{IO}(I,[a])\)) of closed (open) connected partial homeomorphisms of the unit interval \(I\) with a fixed point \(a\in I\). We describe left and right ideals of \(\mathfrak{IC}(I,[0])\) and the Green's relations on \(\math...
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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua:article-6802018-04-04T09:31:27Z On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point Chuchman, Ivan Semigroup of bijective partial transformations, symmetric inverse semigroup, semigroup of homeomorphisms, group congruence, bisimple semigroup 20M20,54H15, 20M18 In this paper we study the semigroup \(\mathfrak{IC}(I,[a])\) (\(\mathfrak{IO}(I,[a])\)) of closed (open) connected partial homeomorphisms of the unit interval \(I\) with a fixed point \(a\in I\). We describe left and right ideals of \(\mathfrak{IC}(I,[0])\) and the Green's relations on \(\mathfrak{IC}(I,[0])\). We show that the semigroup \(\mathfrak{IC}(I,[0])\) is bisimple and every non-trivial congruence on \(\mathfrak{IC}(I,[0])\) is a group congruence. Also we prove that the semigroup \(\mathfrak{IC}(I,[0])\) is isomorphic to the semigroup \(\mathfrak{IO}(I,[0])\) and describe the structure of a semigroup \(\mathfrak{II}(I,[0])=\mathfrak{IC}(I,[0])\sqcup \mathfrak{IO}(I,[0])\). As a corollary we get structures of semigroups \(\mathfrak{IC}(I,[a])\) and \(\mathfrak{IO}(I,[a])\) for an interior point \(a\in I\). Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/680 Algebra and Discrete Mathematics; Vol 12, No 2 (2011) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/680/214 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-04-04T09:31:27Z |
| collection |
OJS |
| language |
English |
| topic |
Semigroup of bijective partial transformations symmetric inverse semigroup semigroup of homeomorphisms group congruence bisimple semigroup 20M20,54H15 20M18 |
| spellingShingle |
Semigroup of bijective partial transformations symmetric inverse semigroup semigroup of homeomorphisms group congruence bisimple semigroup 20M20,54H15 20M18 Chuchman, Ivan On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point |
| topic_facet |
Semigroup of bijective partial transformations symmetric inverse semigroup semigroup of homeomorphisms group congruence bisimple semigroup 20M20,54H15 20M18 |
| format |
Article |
| author |
Chuchman, Ivan |
| author_facet |
Chuchman, Ivan |
| author_sort |
Chuchman, Ivan |
| title |
On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point |
| 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 |
| description |
In this paper we study the semigroup \(\mathfrak{IC}(I,[a])\) (\(\mathfrak{IO}(I,[a])\)) of closed (open) connected partial homeomorphisms of the unit interval \(I\) with a fixed point \(a\in I\). We describe left and right ideals of \(\mathfrak{IC}(I,[0])\) and the Green's relations on \(\mathfrak{IC}(I,[0])\). We show that the semigroup \(\mathfrak{IC}(I,[0])\) is bisimple and every non-trivial congruence on \(\mathfrak{IC}(I,[0])\) is a group congruence. Also we prove that the semigroup \(\mathfrak{IC}(I,[0])\) is isomorphic to the semigroup \(\mathfrak{IO}(I,[0])\) and describe the structure of a semigroup \(\mathfrak{II}(I,[0])=\mathfrak{IC}(I,[0])\sqcup \mathfrak{IO}(I,[0])\). As a corollary we get structures of semigroups \(\mathfrak{IC}(I,[a])\) and \(\mathfrak{IO}(I,[a])\) for an interior point \(a\in I\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/680 |
| work_keys_str_mv |
AT chuchmanivan onasemigroupofclosedconnectedpartialhomeomorphismsoftheunitintervalwithafixedpoint |
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2025-07-17T10:31:27Z |
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2025-07-17T10:31:27Z |
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1837890137792446464 |