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.
@article{bwmeta1.element.bwnjournal-article-apmv59z2p171bwm,
author = {Gianluca Gorni and Gaetano Zampieri},
title = {Injectivity onto a star-shaped set for local homeomorphisms in n-space},
journal = {Annales Polonici Mathematici},
volume = {60},
year = {1994},
pages = {171-196},
zbl = {0814.58009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv59z2p171bwm}
}
Gianluca Gorni; Gaetano Zampieri. Injectivity onto a star-shaped set for local homeomorphisms in n-space. Annales Polonici Mathematici, Tome 60 (1994) pp. 171-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv59z2p171bwm/
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