On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point
In this paper we study the semigroup IC(I,[a]) (IO(I,[a])) of closed (open) connected partial homeomorphisms of the unit interval I with a fixed point a∈I. We describe left and right ideals of IC(I,[0]) and the Green's relations on IC(I,[0]). We show that the semigroup IC(I,[0]) is bisimple and...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/154866 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point / I. Chuchman // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 2. — С. 38–52. — Бібліогр.: 10 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730028799754240 |
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| author | Chuchman, I. |
| author_facet | Chuchman, I. |
| citation_txt | On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point / I. Chuchman // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 2. — С. 38–52. — Бібліогр.: 10 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | In this paper we study the semigroup IC(I,[a]) (IO(I,[a])) of closed (open) connected partial homeomorphisms of the unit interval I with a fixed point a∈I. We describe left and right ideals of IC(I,[0]) and the Green's relations on IC(I,[0]). We show that the semigroup IC(I,[0]) is bisimple and every non-trivial congruence on IC(I,[0]) is a group congruence. Also we prove that the semigroup IC(I,[0]) is isomorphic to the semigroup IO(I,[0]) and describe the structure of a semigroup II(I,[0])=IC(I,[0])⊔IO(I,[0]). As a corollary we get structures of semigroups IC(I,[a]) and IO(I,[a]) for an interior point a∈I.
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| first_indexed | 2025-12-07T19:17:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154866 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:17:37Z |
| publishDate | 2011 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Chuchman, I. 2019-06-16T05:51:42Z 2019-06-16T05:51:42Z 2011 On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point / I. Chuchman // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 2. — С. 38–52. — Бібліогр.: 10 назв. — англ. 1726-3255 2010 Mathematics Subject Classification:20M20,54H15, 20M18. https://nasplib.isofts.kiev.ua/handle/123456789/154866 In this paper we study the semigroup IC(I,[a]) (IO(I,[a])) of closed (open) connected partial homeomorphisms of the unit interval I with a fixed point a∈I. We describe left and right ideals of IC(I,[0]) and the Green's relations on IC(I,[0]). We show that the semigroup IC(I,[0]) is bisimple and every non-trivial congruence on IC(I,[0]) is a group congruence. Also we prove that the semigroup IC(I,[0]) is isomorphic to the semigroup IO(I,[0]) and describe the structure of a semigroup II(I,[0])=IC(I,[0])⊔IO(I,[0]). As a corollary we get structures of semigroups IC(I,[a]) and IO(I,[a]) for an interior point a∈I. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point Article published earlier |
| spellingShingle | On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point Chuchman, I. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154866 |
| work_keys_str_mv | AT chuchmani onasemigroupofclosedconnectedpartialhomeomorphismsoftheunitintervalwithafixedpoint |