Abstract
Every real function continuous on a closed interval is representable as a convergent sequence of step functions defined by an R-converter. Deterministic and nondeterministic R-converters are considered with the corresponding classes of operators that they define in the Cantor space. It is shown that the problem of finding the roots of the equation f(x) = 0 for a continuous and sign-constant function on [0, 1] cannot be solved by a deterministic R-converter, while a nondeterministic R-converter produces a solution of this problem.
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Additional information
Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 68, pp. 129–136, 1989.
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Lisovik, L.P. Properties of Δ-functions. J Math Sci 69, 1472–1475 (1994). https://doi.org/10.1007/BF01250594
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DOI: https://doi.org/10.1007/BF01250594