Conclusions
15. According to the methods of § 3 and § 4, we are considering the solution on a bicompact set M, taking as approximate solutions the elements of this set, i.e., we restrict X to a bicompact space M.
By virtue of the corollary of Theorem 5, this re-establishes the stability of the problem. Thus by using bicompact sets and the related additional information about the solution, it is possible to go over from an incorrect problem to a problem which is correct in the sense of Tikhonov (see [19], p. 4).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 10, No. 5, pp. 1065–1074, September–October, 1969.
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Ivanov, V.K. Incorrect problems in topological spaces. Sib Math J 10, 785–791 (1969). https://doi.org/10.1007/BF00971654
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DOI: https://doi.org/10.1007/BF00971654