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

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Gorni G., Zampieri G.

Annales Polonici Mathematici

1994

tom 59

nr 2

171-196

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Gorni G.

1 Zampieri G.

1 1994

Wyniki wyszukiwania

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