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

Fundamenta Mathematicae (1998)

- Volume: 155, Issue: 2, page 161-176
- ISSN: 0016-2736

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topHagopian, Charles. "The fixed-point property for deformations of tree-like continua." Fundamenta Mathematicae 155.2 (1998): 161-176. <http://eudml.org/doc/212249>.

@article{Hagopian1998,

abstract = {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.},

author = {Hagopian, Charles},

journal = {Fundamenta Mathematicae},

keywords = {fixed point; arc-component; deformation; tree-like continuum; Borsuk ray; dog-chases-rabbit argument; JFM 40.0372.03},

language = {eng},

number = {2},

pages = {161-176},

title = {The fixed-point property for deformations of tree-like continua},

url = {http://eudml.org/doc/212249},

volume = {155},

year = {1998},

}

TY - JOUR

AU - Hagopian, Charles

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

JO - Fundamenta Mathematicae

PY - 1998

VL - 155

IS - 2

SP - 161

EP - 176

AB - 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.

LA - eng

KW - fixed point; arc-component; deformation; tree-like continuum; Borsuk ray; dog-chases-rabbit argument; JFM 40.0372.03

UR - http://eudml.org/doc/212249

ER -

## References

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