Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 5 min ago
PreprintCC BY 4.0arXiv

n-Scrambled Cantor sets

  • B. Miller
Open at sourcePDFDOICite

Abstract

For all n ≥ 2, we obtain a homeomorphism of Cantor space that has a distributionally n-scrambled Cantor set containing a distributionally (n+1)-scrambled uncountable set, but does not have an (n+1)-scrambled Cantor set.

Related

  1. Favard length of non-homogeneous random disc-like Cantor sets
    Alan Chang, Damian Dąbrowski, Giacomo Del Nin
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. Solutions of xα+yα=1 in λ-Cantor sets
    Kan Jiang, Nero Ziyu Li, Lifeng Xi
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryDynamical systemsarXiv
  3. Thompson's groups and Teichmüller modular groups of generalized Cantor sets
    Hiroshige Shiga
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  4. On Sums of "Small" Cantor Sets
    Anton Gorodetski, Alexandro Luna, William Wood
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  5. On various notions of universally Baire sets and reflection of non-Baire property in Cantor sets
    Márton Elekes, Máté Pálfy
    arXivPreprintarXiv licenceFull textGeometry & topologyLogic & foundationsarXiv

Cite

BibTeXRIS
BibTeX
@misc{miller2026nscrambled,
  title = {{n-Scrambled Cantor sets}},
  author = {B. Miller},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00514},
  eprint = {2609.00514},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00514},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - n-Scrambled Cantor sets
AU  - B. Miller
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.00514
UR  - https://arxiv.org/abs/2609.00514
AB  - For all n ≥ 2, we obtain a homeomorphism of Cantor space that has a distributionally n-scrambled Cantor set containing a distributionally (n+1)-scrambled uncountable set, but does not have an (n+1)-scrambled Cantor set.
ER  -