Geodesic
Quasivarieties of Metric Algebras
Algebra i logika, Tome 42 (2003) no. 6, pp. 747-762

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We introduce concepts of a continuous family of quasi-identities and of a continuous quasivariety. For continuous quasivarieties, a characterization theorem and an analog of the Birkhoff theorem on subdirect decomposition are proved. Also we point out the way of constructing examples of continuous quasivarieties and furnish the characterization of a relative congruence lattice of systems in the quasivarieties in question. Lastly, we re-prove the Hahn–Banach theorem on extension of a linear functional.
Keywords: metric algebra, relative quasivariety, congruence lattice. 
@article{AL_2003_42_6_a7,
     author = {V. A. Khudyakov},
     title = {Quasivarieties of {Metric} {Algebras}},
     journal = {Algebra i logika},
     pages = {747--762},
     publisher = {mathdoc},
     volume = {42},
     number = {6},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2003_42_6_a7/}
}
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V. A. Khudyakov. Quasivarieties of Metric Algebras. Algebra i logika, Tome 42 (2003) no. 6, pp. 747-762. http://geodesic.mathdoc.fr/item/AL_2003_42_6_a7/