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

• Date: 2018
• 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
• Journal Title: Algebra and Discrete Mathematics

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...