The Space-filling Curve of Hilbcrt cube
碩士 === 國立中山大學 === 應用數學系 === 87 === Let $M$ be a compact connected topological manifold of finite or infinite dimension. We construct mechanically a space-filling curve $f$ of $M$. Moreover, for any number $r$ between 0 and 1, there is a compact subset $A$ of the unit interval $[0,1]$ of H...
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| Format: | Others |
| Language: | en_US |
| Published: |
1999
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| Online Access: | http://ndltd.ncl.edu.tw/handle/20008543532553480272 |
| Summary: | 碩士 === 國立中山大學 === 應用數學系 === 87 === Let $M$ be a compact connected topological manifold of finite or infinite dimension. We construct mechanically a space-filling curve $f$ of $M$. Moreover, for any number $r$ between 0 and 1, there is a compact subset $A$ of the unit interval $[0,1]$ of Hausdorff dimension $r$ such that $f(A)$ fills all of $M$. The proof is based on a special case in which the Hilbert cube $[0,1]^{\om}$ is filled by one of such curves.
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