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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2018, Number 1, Pages 92–119
(Mi basm469)
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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.
Received: 11.03.2018
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
Linking options:
https://www.mathnet.ru/eng/basm469 https://www.mathnet.ru/eng/basm/y2018/i1/p92
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Abstract page: | 220 | Full-text PDF : | 68 | References: | 17 |
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