The fixed-point property for deformations of tree-like continua

• Autorzy: Charles L. Hagopian
• Języki publikacji: EN

Abstrakty

EN

Let f be a map of a tree-like continuum M that sends each arc-component of M into itself. We prove that f has a fixed point. Hence every tree-like continuum has the fixed-point property for deformations (maps that are homotopic to the identity). This result answers a question of Bellamy. Our proof resembles an old argument of Brouwer involving uncountably many tangent curves. The curves used by Brouwer were originally defined by Peano. In place of these curves, we use rays that were originally defined by Borsuk.

Słowa kluczowe

EN

fixed point; arc-component; deformation; tree-like continuum; Borsuk ray; dog-chases-rabbit argument

Kategorie tematyczne

• 54F15: Continua and generalizations
• 54H25: Fixed-point and coincidence theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 155
• Numer: 2
• Strony: 161-176

Daty

wydano

1998

otrzymano

1996-09-18

Twórcy

autor

Charles L. Hagopian

• Department of Mathematics, California State University, Sacramento, California 95819, U.S.A.

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