Strong porosity features of typical continuous functions

DOI10.1007/BF01955016zbMath0592.26010OpenAlexW2018215551MaRDI QIDQ1075448

Andrew M. Bruckner, John Haussermann

Publication date: 1985

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01955016

zbMATH Keywords

Rnowhere differentiable functionsresidual settypical continuous functionbilaterally strongly porous subsets ofpath-differentiation

Mathematics Subject Classification ID

Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Related Items

Porosity, derived numbers and knot points of typical continuous functions ⋮ Multifractal Properties of Convex Hulls of Typical Continuous Functions ⋮ Attractive properties via generalized derivatives of continuous functions ⋮ Some further typical results on bounded Baire one functions

Cites Work

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• Differentiable restrictions of continuous functions
• Current trends in differentiation theory
• Path Derivatives: A Unified View of Certain Generalized Derivatives
• The Level Structure of a Residual Set of Continuous Functions
• Sur les fonctions non dérivables
• Über die Differenzierbarkeit stetiger Funktionen
• Sur les nombres dérivés
• On the Differentiability Structure of Real Functions

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