RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Bul. Acad. Ştiinţe Repub. Mold. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, Number 1, Pages 92–119 (Mi basm469)  

Distances on free semigroups and their applications

M. M. Chobana, I. A. Budanaevb

a Tiraspol State University, Republic of Moldova, str. Iablochkin 5, Chisinau, Moldova
b Institute of Mathematics and Computer Sciences of ASM, str. Academiei, 3/2, MD-2028, Chisinau, Moldova

Abstract: In this article it is proved that for any quasimetric $d$ on a set $X$ with a base-point $p_X$ there exists a maximal invariant extension $\hat\rho$ on the free monoid $F^a(X,\mathcal V)$ in a non-Burnside quasi-variety $\mathcal V$ of topological monoids (Theorem 6.1). This fact permits to prove that for any non-Burnside quasi-variety $\mathcal V$ of topological monoids and any $T_0$-space $X$ the free topological monoid $F(X,\mathcal V)$ exists and is abstract free (Theorem 7.1). Corollary 10.2 affirms that $F(X,\mathcal V)$, where $\mathcal V$ is a non-trivial complete non-Burnside quasi-variety of topological monoids, is a topological digital space if and only if $X$ is a topological digital space.

Keywords and phrases: quasi-variety of topological monoids, free monoid, invariant distance, quasimetric.

Full text: PDF file (273 kB)
References: PDF file   HTML file

MSC: 20M05, 20M07, 32F45, 522A15, 4E25, 54E35, 54H15, 20F10
Received: 11.03.2018
Language:

Citation: M. M. Choban, I. A. Budanaev, “Distances on free semigroups and their applications”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, no. 1, 92–119

Citation in format AMSBIB
\Bibitem{ChoBud18}
\by M.~M.~Choban, I.~A.~Budanaev
\paper Distances on free semigroups and their applications
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2018
\issue 1
\pages 92--119
\mathnet{http://mi.mathnet.ru/basm469}


Linking options:
  • http://mi.mathnet.ru/eng/basm469
  • http://mi.mathnet.ru/eng/basm/y2018/i1/p92

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
    Number of views:
    This page:76
    Full text:30
    References:7

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019