A minimum theorem for n-valued multifunctions

Helga Schirmer

Displaying similar documents to “A minimum theorem for n-valued multifunctions”

An index and a Nielsen number for n-valued multifunctions

Helga Schirmer (1984)

Fundamenta Mathematicae

Similarity:

The least number of fixed points of bimaps

Helga Schirmer (1991)

Fundamenta Mathematicae

Similarity:

Fixed Points of n-Valued Multimaps of the Circle

Robert F. Brown (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

A multifunction ϕ: X ⊸ Y is n-valued if ϕ(x) is an unordered subset of n points of Y for each x ∈ X. The (continuous) n-valued multimaps ϕ: S¹ ⊸ S¹ are classified up to homotopy by an integer-valued degree. In the Nielsen fixed point theory of such multimaps, due to Schirmer, the Nielsen number N(ϕ) of an n-valued ϕ: S¹ ⊸ S¹ of degree d equals |n - d| and ϕ is homotopic to an n-valued power map that has exactly |n - d| fixed points. Thus the Wecken property, that Schirmer established...