O вычислимой сводимости метрик на вещественных числах
Algebra i logika, Tome 61 (2022) no. 1, pp. 98-110.

Voir la notice de l'article provenant de la source Math-Net.Ru

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R. A. Kornev. O вычислимой сводимости метрик на вещественных числах. Algebra i logika, Tome 61 (2022) no. 1, pp. 98-110. http://geodesic.mathdoc.fr/item/AL_2022_61_1_a5/

[1] R. M. Robinson, “Review of R. Peter's book, "‘Rekursive Funktionen"’”, J. Symb. Log., 16 (1951), 280–282

[2] K. Ko, “On the continued fraction representation of computable real numbers”, Theor. Comput. Sci., 47 (1986), 299–313

[3] A. M. Turing, “On computable numbers, with an application to the Entscheidungsproblem. A correction”, Proc. Lond. Math. Soc., II. Ser., 43 (1937), 544–546

[4] K. Weihrauch, Ch. Kreitz, “Representations of the real numbers and of the open subsets of the set of real numbers”, Ann. Pure Appl. Logic, 35 (1987), 247–260

[5] K. Weihrauch, “Type 2 recursion theory”, Theor. Comput. Sci., 38 (1985), 17–33

[6] Ch. Kreitz, K. Weihrauch, “Theory of representations”, Theor. Comput. Sci., 38 (1985), 35–53

[7] Yu. L. Ershov, Teoriya numeratsii, Nauka, M., 1977

[8] Yu. L. Ershov, “Theory of numberings”, Handbook of computability theory, Stud. Logic Found. Math., 140, ed. E. R. Griffor, Elsevier, Amsterdam, 1999, 473–503

[9] M. B. Pour-El, J. I. Richards, Computability in analysis and physics, Springer-Verlag, Berlin, 1989

[10] T. Mori, Y. Tsujii, M. Yasugi, “Computability structures on metric spaces”, Combinatorics, complexity and logic, DMTCS'96, Proc. 1st int. conf. discr. math. theor. comput. sci. (Auckland, New Zealand, December 9-13, 1996), eds. Bridges et al., Springer, Berlin, 1997, 351–362

[11] M. Yasugi, T. Mori, Y. Tsujii, “Effective properties of sets and functions in metric spaces with computability structure”, Theor. Comput. Sci., 219:1/2 (1999), 467–486

[12] Z. Iljazović, “Isometries and computability structures”, J. UCS, 16:18 (2010), 2569–2596

[13] A. G. Melnikov, “Computably isometric spaces”, J. Symb. Log., 78:4 (2013), 1055–1085

[14] T. H. McNicholl, “Computable copies of $\ell^{p^1}$”, Computability, 6:4 (2017), 391–408

[15] K. Weihrauch, Computable analysis. An introduction, Texts Theor. Comput. Sci., EATCS Ser., Springer, Berlin, 2000

[16] R. Dillhage, Computable functional analysis. Compact operators on computable Banach spaces and computable best approximation, PhD thesis, Fak. Math. Inform., Fern Universität Hagen, 2012

[17] R. A. Kornev, “Svodimost vychislimykh metrik na veschestvennoi pryamoi”, Algebra i logika, 56:4 (2017), 453–476

[18] R. Kornev, “Computable metrics above the standard real metric”, Sib. elektron. matem. izv., 18:1 (2021), 377–392 http://semr.math.nsc.ru/v18/n1/p377-392.pdf

[19] R. A. Kornev, “Polureshetka stepenei vychislimykh metrik”, Sib. matem. zh., 62:5 (2021), 1013–1038

[20] R. Kornev, “On the maximality of degrees of metrics under computable reducibility”, Sib. elektron. matem. izv., 19:1 (2022), 248–258 http://semr.math.nsc.ru/v19/n1/p248-258.pdf