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...
Gespeichert in:
| Datum: | 2018 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/680 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| _version_ | 1856543356755116032 |
|---|---|
| author | Chuchman, Ivan |
| author_facet | Chuchman, Ivan |
| author_sort | Chuchman, Ivan |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T09:31:27Z |
| 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 \(a\in I\). |
| first_indexed | 2026-02-08T07:57:59Z |
| format | Article |
| id | admjournalluguniveduua-article-680 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:59Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| 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 |
| title | 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_short | 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 |
| topic | Semigroup of bijective partial transformations symmetric inverse semigroup semigroup of homeomorphisms group congruence bisimple semigroup 20M20,54H15 20M18 |
| topic_facet | Semigroup of bijective partial transformations symmetric inverse semigroup semigroup of homeomorphisms group congruence bisimple semigroup 20M20,54H15 20M18 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/680 |
| work_keys_str_mv | AT chuchmanivan onasemigroupofclosedconnectedpartialhomeomorphismsoftheunitintervalwithafixedpoint |