Dimension and structure of typical compact sets, continua and curves

DOI10.1007/BF01308668zbMath0666.28005OpenAlexW2091649414MaRDI QIDQ1117053

Peter M. Gruber

Publication date: 1989

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178442

zbMATH Keywords

Hausdorff dimensioncurvesporosityentropy dimensioncontinuathinnessgraphs of real continuous functionstypical compact sets

Mathematics Subject Classification ID

Entropy and other invariants (28D20) Integration of real functions of several variables: length, area, volume (26B15) Dimension theory in general topology (54F45) Hausdorff and packing measures (28A78) Classification of real functions; Baire classification of sets and functions (26A21) Topology of special sets defined by functions (54C50)

Related Items (16)

Typical dimension of the graph of certain functions ⋮ Fractal boundaries are not typical ⋮ Unnamed Item ⋮ Generic Properties of Compact Starshaped Sets ⋮ On the Hausdorff and packing measures of typical compact metric spaces ⋮ On typical compact submanifolds of the Euclidean space ⋮ Typical elements and meager spaces ⋮ A note on the interior and dimensions of typical sumsets ⋮ Porosity and unique completion in strictly convex spaces ⋮ Exceptional Sets for Universally Polygonally Approximable Functions ⋮ Some New Concepts of Dimension ⋮ Average box dimensions of typical compact sets ⋮ Generic properties of compact metric spaces ⋮ On typical sets in Banach spaces and a parametric Kuratowski-Ulam theorem ⋮ Contrasting Symmetric Porosity and Porosity ⋮ On average Hewitt-Stromberg measures of typical compact metric spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The convex hull of a typical compact set
• How Many Sets are Porous?
• Families of compact sets and their universals
• Hausdorff Measure, Entropy, and the Independence of Small Sets
• Generic Properties of Compact Starshaped Sets
• BOUNDARY PROPERTIES OF ARBITRARY FUNCTIONS
• Sets of Fractional Dimensions (V): on Dimensional Numbers of Some Continuous Curves
• Topologies on Spaces of Subsets

This page was built for publication: Dimension and structure of typical compact sets, continua and curves