On monoids of injective partial selfmaps almost everywhere the identity

Demonstratio mathematica

article

Ivan Chuchman¹  Oleg Gutik¹ 

[1] Department of Mechanics and Mathematics, Ivan Franko Lviv National University

关键词: topological semigroup;    semitopological semigroup;    topological inverse semigroup;    semigroup of bijective partial transformations;    symmetric inverse semigroup;    free semilattice;    ideal;    congruence;    semigroup with the F-property;    Baire space;    hereditary Baire space;    embedding;   

DOI  :  10.1515/dema-2013-0340

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

In this paper we study the semigroup ℐλ∞${\cal I}_\lambda ^\infty $ of injective partial selfmaps almost everywhere the identity of a set of infinite cardinality λ . We describe the Green relations on ℐλ∞${\cal I}_\lambda ^\infty $, all (two-sided) ideals and all congruences of the semigroup ℐλ∞${\cal I}_\lambda ^\infty $. We prove that every Hausdorff hereditary Baire topology τ on ℐλ∞${\cal I}_\lambda ^\infty $ such that (ℐλ∞${\cal I}_\lambda ^\infty $, τ ) is a semitopological semigroup is discrete and describe the closure of the discrete semigroup ℐλ∞${\cal I}_\lambda ^\infty $ in a topological semigroup. Also we show that for an infinite cardinal λ the discrete semigroup ℐλ∞${\cal I}_\lambda ^\infty $ does not embed into a compact topological semigroup and construct two non-discrete Hausdorff topologies turning ℐλ∞${\cal I}_\lambda ^\infty $ into a topological inverse semigroup.

【 授权许可】

CC BY