A reduction of the Nielsen fixed point theorem for symmetric product maps to the Lefschetz theorem
A fixed point conjecture for Borsuk continuous set-valued mappings
The main result of this paper is that for n = 3,4,5 and k = n-2, every Borsuk continuous set-valued map of the closed ball in the n-dimensional Euclidean space with values which are one-point sets or sets homeomorphic to the k-sphere has a fixed point. Our approach fails for (k,n) = (1,4). A relevant counterexample (for the homological method, not for the fixed point conjecture) is indicated.
An Application of the Stiefel-Whitney Classes to the Proof of a Fixed Point Theorem for Set-Valued Mappings
We prove a fixed point theorem for Borsuk continuous mappings with spherical values, which extends a previous result. We apply some nonstandard properties of the Stiefel-Whitney classes.
The Brouwer Fixed Point Theorem for Some Set Mappings
For some classes of closed subsets of the disc ₙ ⊂ ℝⁿ we prove that every Hausdorff-continuous mapping f: X → X has a fixed point A ∈ X in the sense that the intersection A ∩ f(A) is nonempty.
Fixed Points of Maps of Sets of Polyhedra into the Disc
We prove that Platonic and some Archimedean polyhedra have the fixed point property in a non-classical sense.
An equation with no -periodic solutions.
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