Controlled Hahn--Mazurkiewicz Theorem and some new dimension functions of Peano continua

DOI10.1016/J.TOPOL.2005.11.018zbMath1140.54015OpenAlexW2056044040MaRDI QIDQ876517

Taras Banakh, Murat Tuncali

Publication date: 18 April 2007

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2005.11.018

zbMATH Keywords

fractal dimensionHölder mapPeano continuum

Mathematics Subject Classification ID

Continua and generalizations (54F15) Dimension theory in general topology (54F45)

Related Items (7)

The shark teeth is a topological IFS-attractor ⋮ A 1-dimensional Peano continuum which is not an IFS attractor ⋮ Counterexamples for IFS-attractors ⋮ Computing space-filling curves ⋮ Addendum to: Characterizations of topological dimension by use of normal sequences of finite open covers and Pontrjagin-Schnirelmann theorem ⋮ Arbitrarily high Hausdorff dimensions of continua ⋮ Cyclic iterated function systems

Cites Work

• One-dimensional continuous curves and a homogeneity theorem
• Spaces of Finite Length
• Partitioning a set
• Grille decomposition and convexification theorems for compact metric locally connected continua
• Continua of Finite Linear Measure I
• Characterizing 𝑘-dimensional universal Menger compacta
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