Constructing space-filling curves of compact connected manifolds

Ying Fen Lin; Ngai Ching Wong

doi:10.1016/S0898-1221(03)90008-3

Constructing space-filling curves of compact connected manifolds

Ying Fen Lin
, Ngai Ching Wong^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	1871-1881
Number of pages	11
Journal	Computers and Mathematics with Applications
Volume	45
Issue number	12
DOIs	https://doi.org/10.1016/S0898-1221(03)90008-3
Publication status	Published - 01 Jun 2003
Externally published	Yes

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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10.1016/S0898-1221(03)90008-3

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title = "Constructing space-filling curves of compact connected manifolds",

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.",

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AU - Lin, Ying Fen

AU - Wong, Ngai Ching

PY - 2003/6/1

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N2 - 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.

AB - 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.

KW - Hausdorff dimensions

KW - Hilbert cube manifolds

KW - Space-filling curves

UR - https://www.scopus.com/pages/publications/0042705546

U2 - 10.1016/S0898-1221(03)90008-3

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M3 - Article

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EP - 1881

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 12

ER -

Constructing space-filling curves of compact connected manifolds

Abstract

Keywords

ASJC Scopus subject areas

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