Constructing space-filling curves of compact connected manifolds

Ying Fen Lin, Ngai Ching Wong*

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let M be a compact connected (topological) manifold of finite- or infinite-dimension n. Let 0 ≤ r ≤ 1 be arbitrary but fixed. We construct in this paper a space-filling curve f from [0, 1] 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 ≤ r ≤ log 2n/log(2n + 2). The proof is based on the special case where M is the Hilbert cube [0, 1]ω.

Original languageEnglish
Pages (from-to)1871-1881
Number of pages11
JournalComputers and Mathematics with Applications
Volume45
Issue number12
DOIs
Publication statusPublished - 01 Jun 2003
Externally publishedYes

Keywords

  • Hausdorff dimensions
  • Hilbert cube manifolds
  • Space-filling curves

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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