Advertisement

Journal of Mathematical Sciences

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

On a Continuity Theorem for Constructive Functions

  • A. A. Vladimirov
Article
  • 32 Downloads

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.

Keywords

Limit Point Arbitrary Point Semantic System Constructive Function Continuity Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    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
  2. 2.
    A. A. Markov, “On the language Lω|,” Dokl. Akad. Nauk SSSR, 215, No. 1, 57–60 (1974).MathSciNetGoogle Scholar
  3. 3.
    A. A. Vladimirov and M. N. Dombrovskii-Kabanchenko, Stratified Semantic System [in Russian], CCAS Publ., Moscow (2009).Google Scholar
  4. 4.
    N. A. Shanin, “A constructive interpretation of mathematical judgments,” Trudy Mat. Inst. Steklov, 52, 226–311 (1958).MATHMathSciNetGoogle Scholar
  5. 5.
    B. A. Kushner, Lectures on Constructive Mathematical Analysis, Amer. Math. Soc., Providence, Rhode Island (1973).Google Scholar
  6. 6.
    N. A. Shanin, “A sketch of a finitary version of mathematical analysis,” Preprint of PDSIM, 06-2000.Google Scholar
  7. 7.
    N. A. Shanin, “Constructive real numbers and constructive functional spaces,” Trudy Mat. Inst. Steklov, 67, 15–294 (1962).MATHMathSciNetGoogle Scholar
  8. 8.
    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

Personalised recommendations