Abstract
It is proved in this article that for Alexander's “horned” sphere S 2A in E3 there exists a pseudoisotopy Ft of the space E3 onto itself which transforms the boundary of the three-dimensional simplexσ 3 in S 2A such that the continuous mapping F1 has a countable set of nondegenerate preimages of points each of which is not a locally connected continuum in E3 intersecting∂σ 3 in a singleton. This answers affirmatively a question posed by R. H. Bing in the Mathematical Congress in Moscow in 1966.
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Translated from Matematicheskie Zametki, Vol. 14, No. 2, pp. 249–259, August, 1973.
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Sandrakova, E.V. Solution of a problem due to Bing. Mathematical Notes of the Academy of Sciences of the USSR 14, 701–706 (1973). https://doi.org/10.1007/BF01147118
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DOI: https://doi.org/10.1007/BF01147118