On Cantor sets with shadows of prescribed dimension

DOI10.1016/j.topol.2012.03.008zbMath1254.46026OpenAlexW2058401552MaRDI QIDQ428813

Maurits van der Meer, Jan J. Dijkstra, Stoyu Barov

Publication date: 25 June 2012

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

Full work available at URL: https://doi.org/10.1016/j.topol.2012.03.008

zbMATH Keywords

shadowHausdorff metricHilbert spaceCantor settopological dimension

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Dimension theory in general topology (54F45)

Related Items (3)

All projections of a typical Cantor set are Cantor sets ⋮ A new simple family of Cantor sets in \(\mathbb{R}^3\) all of whose projections are one-dimensional ⋮ Cantor sets with high-dimensional projections

Cites Work

• Unnamed Item
• On compacta with convex projections
• A Cantor set in \(\mathbb R^d\) with ``large projections
• ON CLOSED SETS IN HILBERT SPACE WITH CONVEX PROJECTIONS UNDER SOMEWHERE DENSE SETS OF DIRECTIONS
• 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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