标题： 相对自由的有限半群范畴的开乘法 显示英文标题

标题： Open multiplication in relatively free profinite semigroupoids

摘要： 本文的目的是将一些有用的结果，例如乘法是开的，在适合的有限生成相对自由的紧半群中已知的结果，扩展到有限顶点图上的相对自由的紧小半群范畴。 这种扩展用于给出无限字母表上重复词的紧性特征，并建立关于相对自由的紧半群和小半群范畴中稳定子的新结果。 显示英文摘要

摘要： The purpose of this paper is to extend some useful results, such as the multiplication being open, previously known for suitable finitely generated relatively free profinite semigroups, to relatively free profinite semigroupoids over finite-vertex graphs. This extension is used to give a profinite characterization of recurrent words over infinite alphabets and to establish new results about stabilizers in relatively free profinite semigroups and semigroupoids.