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1994 | 59 | 2 | 171-196
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Injectivity onto a star-shaped set for local homeomorphisms in n-space

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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.
Opis fizyczny
  • Dipartimento di Matematica e Informatica, Università di Udine, via Zanon 6, 33100 Udine, Italy
  • Dipartimento di Matematica, Pura e Applicata, Università di Padova, via Belzoni 7, 35131 Padova, Italy
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