Continuous maps that preserve Hausdorff measure

Da Wen Deng; Yulan Huang; Sze Man Ngai

doi:10.1016/j.jmaa.2022.126485

Continuous maps that preserve Hausdorff measure

Da Wen Deng
, Yulan Huang
, Sze Man Ngai

Mathematical Sciences

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

Abstract

We show that the space of homeomorphisms on the unit interval [0,1], equipped with the topology of uniform convergence, contains a dense subspace of functions that preserve the Hausdorff measure of any subset of certain one-dimensional self-similar sets. We extend the results to a class of Cantor dust type self-similar sets in R².

Original language	English
Article number	126485
Journal	Journal of Mathematical Analysis and Applications
Volume	516
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2022.126485
State	Published - Dec 1 2022

Scopus Subject Areas

Analysis
Applied Mathematics

Keywords

Cantor dust
Cantor set
Hausdorff measure
Homeomorphism
Self-similar set

Access to Document

10.1016/j.jmaa.2022.126485

Cite this

@article{de18a40c014d42de8f9c6bf857767556,

title = "Continuous maps that preserve Hausdorff measure",

abstract = "We show that the space of homeomorphisms on the unit interval [0,1], equipped with the topology of uniform convergence, contains a dense subspace of functions that preserve the Hausdorff measure of any subset of certain one-dimensional self-similar sets. We extend the results to a class of Cantor dust type self-similar sets in R2.",

keywords = "Cantor dust, Cantor set, Hausdorff measure, Homeomorphism, Self-similar set",

author = "Deng, \{Da Wen\} and Yulan Huang and Ngai, \{Sze Man\}",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2022",

month = dec,

day = "1",

doi = "10.1016/j.jmaa.2022.126485",

language = "English",

volume = "516",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Continuous maps that preserve Hausdorff measure

AU - Deng, Da Wen

AU - Huang, Yulan

AU - Ngai, Sze Man

PY - 2022/12/1

Y1 - 2022/12/1

N2 - We show that the space of homeomorphisms on the unit interval [0,1], equipped with the topology of uniform convergence, contains a dense subspace of functions that preserve the Hausdorff measure of any subset of certain one-dimensional self-similar sets. We extend the results to a class of Cantor dust type self-similar sets in R2.

AB - We show that the space of homeomorphisms on the unit interval [0,1], equipped with the topology of uniform convergence, contains a dense subspace of functions that preserve the Hausdorff measure of any subset of certain one-dimensional self-similar sets. We extend the results to a class of Cantor dust type self-similar sets in R2.

KW - Cantor dust

KW - Cantor set

KW - Hausdorff measure

KW - Homeomorphism

KW - Self-similar set

UR - https://www.scopus.com/pages/publications/85134382447

U2 - 10.1016/j.jmaa.2022.126485

DO - 10.1016/j.jmaa.2022.126485

M3 - Article

AN - SCOPUS:85134382447

SN - 0022-247X

VL - 516

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

M1 - 126485

ER -

Continuous maps that preserve Hausdorff measure

Abstract

Scopus Subject Areas

Keywords

Access to Document

Other files and links

Fingerprint

Cite this