Abstract
A general theorem is proved describing convergence and divergence sets of real continuous functions defined on a metric space E. A result is obtained that is new even for E=[0,1] with distance ρ(x, y)=¦x−y¦.
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Translated from Matematicheskie Zametki, Vol. 17, No. 2, pp. 205–217, February, 1975.
In conclusion the author wishes to thank P. L. Ul'yanov for suggesting this problem and for directing the work.
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Lunina, M.A. Convergence and divergence sets of sequences of real continuous functions on a metric space. Mathematical Notes of the Academy of Sciences of the USSR 17, 120–126 (1975). https://doi.org/10.1007/BF01161867
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DOI: https://doi.org/10.1007/BF01161867