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Algebra and Discrete Mathematics, 2011, том 12, выпуск 2, страницы 38–52
(Mi adm127)
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RESEARCH ARTICLE
On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point
Ivan Chuchman Department of Mechanics and Mathematics, Ivan Franko Lviv National University, Universytetska 1, Lviv, 79000, Ukraine
Аннотация:
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 $a\in I$.
Ключевые слова:
Semigroup of bijective partial transformations, symmetric inverse semigroup, semigroup of homeomorphisms, group congruence, bisimple semigroup.
Поступила в редакцию: 22.09.2011 Исправленный вариант: 22.09.2011
Образец цитирования:
Ivan Chuchman, “On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point”, Algebra Discrete Math., 12:2 (2011), 38–52
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm127 https://www.mathnet.ru/rus/adm/v12/i2/p38
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