The Effectively Enumerable Topological Spaces
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 2, pp. 74-83 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we give a positive answer to the question proposed by Dana Scott on existence of a class of topological spaces which contains the computable metric spaces,the effective $\omega$-continuous domains as proper subclasses and for which computability coincides with effective continuity. In this paper we introduce and investigate the class of effectively enumerable topological spaces which satisfy these requirements.
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M. V. Korovina; O. V. Kudinov. The Effectively Enumerable Topological Spaces. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 2, pp. 74-83. http://geodesic.mathdoc.fr/item/VNGU_2008_8_2_a6/

[1] Abramsky S., Jung A., “Domain Theory”, Handbook of Logic in Computer Science, eds. S. Abramsky, D. Gabbay, T. S. E. Maibaum, Oxford Univ. Press, Oxford, 1994, 1–168 | MR

[2] Brattka V., Presser G., “Computability on Subsets of Metric Spaces”, Theor. Comput. Sci., 305:1–3 (2003), 43–76 | DOI | MR | Zbl

[3] Edalat A., Sönderhauf P., “A Domain-theoretic Approach to Real Number Computation”, Theor. Comput. Sci., 210 (1998), 73–98 | DOI | MR

[4] Ershov Yu. L., Numbering Theorey, Nauka, M., 1977 (in Russian) | MR

[5] Ershov Yu. L., “Model $\mathbb{C}$ of Partial Continuous Functionals”, Logic Colloquium, 76, North-Holland, Amsterdam, 1977, 455–467 | MR

[6] Gierz G., Hofmann K. H., Keimel K. et al., Continuous Lattices and Domains, Cambridge Univ. Press, Cambridge, 2003 | MR | Zbl

[7] Korovina M., Kudinov O., “The Uniformity Principle for $\Sigma$-definability with Applications to Computable Analysis”, CiE'07, Lecture Notes in Computer Science, 4497, eds. S. B. Cooper, B. Löwe, A. Sorbi, Springer, 2007, 416–425 | DOI | MR | Zbl

[8] Korovina M., Kudinov O., “Basic Principles of $\Sigma$-definability and Abstract Computability”, Fachbereich Mathematik, 2008, no. 08-01, 1–24

[9] Korovina M., Kudinov O., “Towards Computability of Higher Type Continuous Data”, CiE, Lecture Notes in Computer Science, 3526, eds. S. B. Cooper, B. Löwe, L. Torenvliet, Springer, 2005, 235–241 | DOI | Zbl

[10] Korovina M., Kudinov O., “Characteristic Properties of Majorant-Computability over the Reals”, CSL, Lecture Notes in Computer Science, 158, eds. G. Gottlob, E. Grandjean, K. Seyr, Springer, 1998, 188–203 | MR

[11] Moschovakis Y. N., “Recursive Metric Spaces”, Fund. Math., 55 (1964), 215–238 | MR | Zbl

[12] Myhill J., Shepherdson J. C., “Effective Operators on Partial Recursive Functions”, Zeitschrift fur Mathematische Logik Grundlagen def Mathematik, 1 (1955), 310–317 | DOI | MR | Zbl

[13] Rogers H. Jr., Theory of Recursive Functions and Effective Computability, McGraw-Hill, N.Y., 1967 | MR | Zbl

[14] Scott D., “Outlines of Mathematical Theory of Computation”, Proc. $4^\textrm{th}$ Annual Princeton Conf. on Information Sciences and Systems, Princeton Univ. Press, Princeton, 1970, 169–176

[15] Spreen D., “On Effective Topological Spaces”, JSL, 63:1 (1998), 185–221 | MR | Zbl

[16] Spreen D., Young P., “Effective Operators in a Topological Setting”, Lecture Notes in Mathematics, 1104, 1984, 436–451 | MR

[17] Weihrauch K., Berechenbarkeit auf cpo's, Schriften zur Angewandten Mathematik und Informatik, 63, Aachen, 1980 | Zbl

[18] Weihrauch K., Computable Analysis, Springer Verlag, Berlin, 2000 | MR | Zbl

[19] Weierstrass K., Sitzungsber. Acad. Berlin, 633:9 (1885), 789–805