Journal of Mathematical Sciences

, Volume 199, Issue 1, pp 6–15 | Cite as

On a Continuity Theorem for Constructive Functions

  • A. A. Vladimirov

We prove that any everywhere defined constructive mapping from a compact metric space into a complete metric space that preserves the precompactness of subsets is uniformly continuous. Bibliography: 8 titles.


Limit Point Arbitrary Point Semantic System Constructive Function Continuity Theorem 
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    B. A. Kushner, “A constructive version of König’s theorem; functions computable in the sense of Markov, Grzegorczyk, and Lacombe,” in: The Theory of Algorithms and Mathematical Logic [in Russian], B. A. Kushner and N. M. Nagorny (eds.), CC AS USSR (1974), pp. 87–111.Google Scholar
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    A. A. Markov, “On the language Lω|,” Dokl. Akad. Nauk SSSR, 215, No. 1, 57–60 (1974).MathSciNetGoogle Scholar
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    A. A. Vladimirov and M. N. Dombrovskii-Kabanchenko, Stratified Semantic System [in Russian], CCAS Publ., Moscow (2009).Google Scholar
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    N. A. Shanin, “Constructive real numbers and constructive functional spaces,” Trudy Mat. Inst. Steklov, 67, 15–294 (1962).MATHMathSciNetGoogle Scholar
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    G. S. Tseitin, “Algorithmic operators in constructive metric spaces,” Trudy Mat. Inst. Steklov, 67, 295–361 (1962).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Dorodnitsyn Computing CenterMoscowRussia

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