Constructing space-filling curves of compact connected manifolds

✍ Scribed by Ying-Fen Lin; Ngai-Ching Wong

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 606 KB
• Volume: 45
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(03)90008-3

✦ Synopsis

Let

M be a compact connected (topological) manifold of finite-or infinite-dimension n. Let 0 < T 5 1 be arbitrary but fixed. We construct in this paper a spac&illing curve f from [0, l] onto M, under which M is the image of a compact set A of Hausdorff dimension r. Moreover, the restriction of f to A is one-to-one over the image of a dense subset provided that 0 < I 5 log2n/log(2n + 2). The proof is based on the special csse where A4 is the Hilbert cube [O,l]".