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Continuity of operators in separable constructive metric spaces

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Abstract

We construct an everywhere defined continuous operator on a separable CMS having the following property: it is not possible to cover the domain of this operator by denumerably many balls such that the oscillation of the operator in each ball of the covering is less than 1.

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Literature cited

  1. G. S. Tseitin, “Algorithmic operators in constructive metric spaces,” Tr. Mat. Inst. Akad. Nauk SSSR,2, 295–361 (1962).

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  2. S. C. Kleene, Introduction to Metamathematics, New York (1952).

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Authors
  1. S. V. Pakhomov
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 60, pp. 194–196, 1976. Results announced October 16, 1975.

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Pakhomov, S.V. Continuity of operators in separable constructive metric spaces. J Math Sci 14, 1554–1556 (1980). https://doi.org/10.1007/BF01693986

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  • DOI: https://doi.org/10.1007/BF01693986

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