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On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point

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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Main Author: Chuchman, Ivan
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
Semigroup of bijective partial transformations
symmetric inverse semigroup
semigroup of homeomorphisms
group congruence
bisimple semigroup
20M20,54H15
20M18
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/680
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spelling 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
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
first_indexed 2024-04-12T06:27:27Z
last_indexed 2024-04-12T06:27:27Z
_version_ 1796109252023025664

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