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EnglishWe 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.
| Titolo: | Injectivity onto a star-shaped set for local homeomorphisms in n-space |
| Autori: | |
| Data di pubblicazione: | 1994 |
| Rivista: | |
| 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. |
| Handle: | http://hdl.handle.net/11562/393334 |
| Appare nelle tipologie: | 01.01 Articolo in Rivista |
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