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- W2055761722 abstract "where p(a, b) means the distance between the points a and b. Their Theorem 4 shows that if E is a finite-dimensional Euclidean space or a real Hilbert space, then for any e-isometry of E into itself, there is an actual isometry of E into itself such that the distance between the images of any point under these two transformations is less than 10e. Their treatment does not concern bounded spaces. The purpose of this paper is to show that the type of k uniformity which Hyers and Ulam obtained in their complete spaces cannot be obtained in general even in very special bounded spaces, but that an -q, e type relation holds for any compact metric space." @default.
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- W2055761722 date "1951-05-01" @default.
- W2055761722 modified "2023-09-25" @default.
- W2055761722 title "Approximate isometries in bounded spaces" @default.
- W2055761722 doi "https://doi.org/10.1090/s0002-9939-1951-0044114-6" @default.
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