Decomposing Euclidean space with a small number of smooth sets

DOI10.1090/S0002-9947-99-02197-2zbMath0916.03033OpenAlexW2169737252MaRDI QIDQ4226683

Juris Steprāns

Publication date: 27 January 1999

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-99-02197-2

zbMATH Keywords

consistencycardinal invariantscontinuous functiondifferentiable functioncovering numbertangent planeSacks realcountable support iterated forcing\(n\)-smooth surfacecontinuously \(n\)-smooth setdecomposition of Euclidean space into smooth surfaces

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Consistency and independence results (03E35) Other combinatorial set theory (03E05) Abstract differentiation theory, differentiation of set functions (28A15)

Related Items (8)

Convexity numbers of closed sets in ℝⁿ ⋮ Differentiability versus continuity: Restriction and extension theorems and monstrous examples ⋮ Sacks forcing, Laver forcing, and Martin's axiom ⋮ CONTINUOUS RAMSEY THEORY ON POLISH SPACES AND COVERING THE PLANE BY FUNCTIONS ⋮ Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle ⋮ A century of Sierpiński-Zygmund functions ⋮ On the number of normal subgroups of an uncountable soluble group ⋮ Discretely normed Abelian groups

Cites Work

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• On the consistency of some partition theorems for continuous colorings, and the structure of \(\aleph _ 1\)-dense real order types
• Proper forcing
• Universal Functions and Generalized Classes of Functions
• Iterated perfect-set forcing
• Decomposing Baire functions
• A very discontinuous Borel function
• On tangents to general sets of points

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