# Injectivity onto a star-shaped set for local homeomorphisms in n-space

Gianluca Gorni; Gaetano Zampieri

Annales Polonici Mathematici (1994)

- Volume: 59, Issue: 2, page 171-196
- ISSN: 0066-2216

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topGianluca Gorni, and Gaetano Zampieri. "Injectivity onto a star-shaped set for local homeomorphisms in n-space." Annales Polonici Mathematici 59.2 (1994): 171-196. <http://eudml.org/doc/262246>.

@article{GianlucaGorni1994,

abstract = {We provide a number of either necessary and sufficient or only sufficient conditions on a local homeomorphism defined on an open, connected subset of the n-space to be actually a homeomorphism onto a star-shaped set. The unifying idea is the existence of "auxiliary" scalar functions that enjoy special behaviours along the paths that result from lifting the half-lines that radiate from a point in the codomain space. In our main result this special behaviour is monotonicity, and the auxiliary function can be seen as a Lyapunov function for a suitable dynamical system having the lifted paths as trajectories.},

author = {Gianluca Gorni, Gaetano Zampieri},

journal = {Annales Polonici Mathematici},

keywords = {global invertibility; local homeomorphisms; star-shaped sets; line-lifting; Lyapunov functions; injectivity; local homeomorphism; star-shaped},

language = {eng},

number = {2},

pages = {171-196},

title = {Injectivity onto a star-shaped set for local homeomorphisms in n-space},

url = {http://eudml.org/doc/262246},

volume = {59},

year = {1994},

}

TY - JOUR

AU - Gianluca Gorni

AU - Gaetano Zampieri

TI - Injectivity onto a star-shaped set for local homeomorphisms in n-space

JO - Annales Polonici Mathematici

PY - 1994

VL - 59

IS - 2

SP - 171

EP - 196

AB - We provide a number of either necessary and sufficient or only sufficient conditions on a local homeomorphism defined on an open, connected subset of the n-space to be actually a homeomorphism onto a star-shaped set. The unifying idea is the existence of "auxiliary" scalar functions that enjoy special behaviours along the paths that result from lifting the half-lines that radiate from a point in the codomain space. In our main result this special behaviour is monotonicity, and the auxiliary function can be seen as a Lyapunov function for a suitable dynamical system having the lifted paths as trajectories.

LA - eng

KW - global invertibility; local homeomorphisms; star-shaped sets; line-lifting; Lyapunov functions; injectivity; local homeomorphism; star-shaped

UR - http://eudml.org/doc/262246

ER -

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