Some mapping theorems for continuous functions defined on the sphere

DOI10.1016/j.na.2011.09.038zbMath1244.55001OpenAlexW2062941276MaRDI QIDQ412635

Yu-Hong Liu

Publication date: 4 May 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2011.09.038

zbMATH Keywords

equivariant mappingfixed point freeKnaster conjectureSmith special index

Mathematics Subject Classification ID

Fixed-point and coincidence theorems (topological aspects) (54H25) Finite groups of transformations in algebraic topology (including Smith theory) (55M35) Fixed points and coincidences in algebraic topology (55M20) Algebraic topology of manifolds (57N65)

Cites Work

• On a property of functions on the sphere and its application
• Borsuk's antipodal theorem for approachable correspondences
• Continuous functions from spheres to Euclidean spaces
• Knaster's problem on continuous maps of a sphere into Euclidean space
• The Knaster problem and the geometry of high-dimensional cubes
• The Knaster problem: more counterexamples
• On a property of functions on a sphere
• Real-Valued Mappings of Spheres
• On Maps From Spheres to Euclidean Spaces
• THE KNASTER PROBLEM AND ALMOST SPHERICAL SECTIONS
• A THEOREM OF BOURGIN-YANG TYPE FOR $ \mathbb{Z}_p^n$-ACTION
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