Proper mappings and dimension

Completely Regular Mappings and Dimension

Supervised dimension reduction mappings

Abstract. We propose a general principle to extend dimension reduction tools to explicit dimension reduction mappings and we show that this can serve as an interface to incorporate prior knowledge in the form of class labels. We explicitly demonstrate this technique by combining locally linear mappings which result from matrix learning vector quantization schemes with the t-distributed stochast...

Proper Holomorphic Mappings in Tetrablock

The theorem showing that there are no non-trivial proper holomorphic self-mappings in the tetrablock is proved. We obtain also some general extension results for proper holomorphic mappings and we prove that the Shilov boundary is invariant under proper holomorphic mappings between some classes of domains containing among others (m1, . . . , mn)-balanced domains. It is also shown that the tetra...

Quasiconformal Mappings Which Increase Dimension

For any compact set E ⊂ R , d ≥ 1 , with Hausdorff dimension 0 < dim(E) < d and for any ε > 0 , there is a quasiconformal mapping (quasisymmetric if d = 1) f of R to itself such that dim(f(E)) > d− ε .

The Bergman Kernel Function and Proper Holomorphic Mappings

It is proved that a proper holomorphic mapping / between bounded complete Reinhardt domains extends holomorphically past the boundary and that if, in addition, /~'(0) = {0}, then / is a polynomial mapping. The proof is accomplished via a transformation rule for the Bergman kernel function under proper holomorphic mappings.