Abstract
We prove that, for any locally connected bounded continuum in the Euclidean space En,n≥2, there exists a sequence of imbeddings of the segment [0, 1] into En uniformly convergent to a continuous mapping of [0, 1] onto this continuum.
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References
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L. V. Keldysh, “Topological imbeddings into Euclidean spaces,”Tr. Mat. Inst. Akad. Nauk SSSR,81 (1966).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 8, pp. 1080–1088, August, 1995.
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Oleksiv, I.Y. Characterization of locally connected continua in Euclidean spaces. Ukr Math J 47, 1234–1243 (1995). https://doi.org/10.1007/BF01057712
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DOI: https://doi.org/10.1007/BF01057712