All projections of a typical Cantor set are Cantor sets

DOI10.1016/j.topol.2020.107192zbMath1472.54016OpenAlexW3015855484MaRDI QIDQ2217231

O. D. Frolkina

Publication date: 29 December 2020

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

Full work available at URL: https://doi.org/10.1016/j.topol.2020.107192

zbMATH Keywords

dimensionEuclidean spaceprojectionCantor setBaire category theorem

Mathematics Subject Classification ID

Baire category, Baire spaces (54E52) Dimension theory in general topology (54F45) Embedding (54C25)

Related Items (1)

A new simple family of Cantor sets in \(\mathbb{R}^3\) all of whose projections are one-dimensional

Cites Work

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• On the space of Cantor subsets of \(\mathbb R^3\)
• On Cantor sets with shadows of prescribed dimension
• On tame Cantor sets in spheres having the same projection in each direction
• Projections of Cantor sets, simple closed curves, and spheres in \(E^3\)
• On compacta with convex projections
• Projections of planar Cantor sets in potential theory
• The structure of typical compact sets in Euclidean space
• Cantor sets with high-dimensional projections
• A Cantor set in \(\mathbb R^d\) with ``large projections
• Some metrics on the subspaces qf a Banach space
• ON CLOSED SETS WITH CONVEX PROJECTIONS
• Raising dimension under all projections
• An example of a simple arc in space whose projection in every plane has interior points

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