The 2-sphere is Wecken for n-valued maps

The 2-sphere is Wecken for n-valued maps

We prove the theorem of the title. Every n -valued map ϕ : S 2 ⊸ S 2 of the 2-sphere has the Wecken property for n -valued maps, that is, it is n -valued homotopic to a map with N ( ϕ ) fixed points, where N ( ϕ ) is the Nielsen number of ϕ .

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Veröffentlicht in:Journal of fixed point theory and applications 2019-06, Vol.21 (2), p.1-6, Article 55
Hauptverfasser: Brown, Robert F., Crabb, Michael, Ericksen, Adam, Stimpson, Matthew
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
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Zusammenfassung:We prove the theorem of the title. Every n -valued map ϕ : S 2 ⊸ S 2 of the 2-sphere has the Wecken property for n -valued maps, that is, it is n -valued homotopic to a map with N ( ϕ ) fixed points, where N ( ϕ ) is the Nielsen number of ϕ .
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-019-0691-1