Distances on Free Semigroups and Their Applications
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2019-02-02 19:20
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512.53+512.548+512.57 (2)
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CHOBAN, Mitrofan; BUDANAEV, Ivan. Distances on Free Semigroups and Their Applications. In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2018, nr. 1(86), pp. 92-119. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Moldovei. Matematica
Numărul 1(86) / 2018 / ISSN 1024-7696

Distances on Free Semigroups and Their Applications


CZU: 512.53+512.548+512.57
MSC 2010: 20M05, 20M07, 32F45, 522A15, 4E25, 54E35, 54H15, 20F10
Pag. 92-119

Choban Mitrofan1, Budanaev Ivan2
 
1 Moldova Tiraspol State University,
2 Institute of Mathematics and Computer Science ASM
 
Disponibil în IBN: 20 august 2018


Rezumat

In this article it is proved that for any quasimetric d on a set X with a base-point pX there exists a maximal invariant extension ˆ_ on the free monoid F a(X, V) in a non-Burnside quasi-variety V of topological monoids (Theorem 6.1). This fact permits to prove that for any non-Burnside quasi-variety V of topological monoids and any T0-space X the free topological monoid F(X,V) exists and is abstract free (Theorem 8.1). Corollary 10.2 affirms that F(X, V), where 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

Cuvinte-cheie
Quasi-variety of topological monoids, free monoid, invariant distance, quasimetric