Some embeddings of infinite-dimensional spaces |
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Authors: | Zahava Shmuely |
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Institution: | (1) Technion, Israel Institute of Technology, Haifa |
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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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Keywords: | |
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