Abstract
It is shown that ifA is a weakly infinite-dimensional subset of a metric spaceR then aG δ setB ofR exists such thatA⊆B andB is weakly infinite-dimensional. A similar result holds for a set having strong transfinite inductive dimension. As a consequence each weakly infinite-dimensional metric space possesses a weakly infinite-dimensional complete metric extension. A similar result holds also for a space having strong transfinite inductive dimension.
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Shmuely, Z. Some embeddings of infinite-dimensional spaces. Isr. J. Math. 12, 5–10 (1972). https://doi.org/10.1007/BF02764807
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DOI: https://doi.org/10.1007/BF02764807