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Epsilon Nielsen coincidence theory

Marcio Fenille — 2014

Open Mathematics

We construct an epsilon coincidence theory which generalizes, in some aspect, the epsilon fixed point theory proposed by Robert Brown in 2006. Given two maps f, g: X → Y from a well-behaved topological space into a metric space, we define µ ∈(f, g) to be the minimum number of coincidence points of any maps f 1 and g 1 such that f 1 is ∈ 1-homotopic to f, g 1 is ∈ 2-homotopic to g and ∈ 1 + ∈ 2 < ∈. We prove that if Y is a closed Riemannian manifold, then it is possible to attain µ ∈(f, g) moving...

Strong surjectivity of maps from 2-complexes into the 2-sphere

Marcio FenilleOziride Neto — 2010

Open Mathematics

Given a model 2-complex K P of a group presentation P, we associate to it an integer matrix ΔP and we prove that a cellular map f: K P → S 2 is root free (is not strongly surjective) if and only if the diophantine linear system ΔP Y = d e g (f) has an integer solution, here d e g (f)is the so-called vector-degree of f

A reverse viewpoint on the upper semicontinuity of multivalued maps

Marcio Colombo Fenille — 2013

Mathematica Bohemica

For a multivalued map ϕ : Y ( X , τ ) between topological spaces, the upper semifinite topology 𝒜 ( τ ) on the power set 𝒜 ( X ) = { A X : A } is such that ϕ is upper semicontinuous if and only if it is continuous when viewed as a singlevalued map ϕ : Y ( 𝒜 ( X ) , 𝒜 ( τ ) ) . In this paper, we seek a result like this from a reverse viewpoint, namely, given a set X and a topology Γ on 𝒜 ( X ) , we consider a natural topology ( Γ ) on X , constructed from Γ satisfying ( Γ ) = τ if Γ = 𝒜 ( τ ) , and we give necessary and sufficient conditions to the upper semicontinuity of a multivalued map ϕ : Y ( X , ( Γ ) ) ...

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