- Tytuł:
- The fixed-point property for deformations of tree-like continua
- Autorzy:
- Hagopian, Charles
- Powiązania:
- https://bibliotekanauki.pl/articles/1205393.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
fixed point
arc-component
deformation
tree-like continuum
Borsuk ray
dog-chases-rabbit argument - Opis:
- 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.
- Źródło:
-
Fundamenta Mathematicae; 1998, 155, 2; 161-176
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł