Displaying similar documents to “On a theorem in the theory of dimensionality”

Dimension and ε -translations

Tatsuo Goto (1996)

Commentationes Mathematicae Universitatis Carolinae

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Some theorems characterizing the metric and covering dimension of arbitrary subspaces in a Euclidean space will be obtained in terms of ε -translations; some of them were proved in our previous paper [G1] under the additional assumption of the boundedness of subspaces.

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

Gianluca Gorni, Gaetano Zampieri (1994)

Annales Polonici Mathematici

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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...