Related papers: Some mapping theorems for extensional dimension
The aim of this paper is to generalize the results on expansive mappings of Yesilkaya and Aydin from \cite{Yesilkaya}. We give some fixed point results for q-expansive mappings in metric spaces and prove some fixed point theorems for this…
In this paper, we consider mappings on uniform domains with exponentially integrable distortion whose Jacobian determinants are integrable. We show that such mappings can be extended to the boundary and moreover these extensions are…
The $\lambda$-perfect maps, a generalization of perfect maps (continuous closed maps with compact fibers) are presented. Using $P_\lambda$-spaces and the concept of $\lambda$-compactness some results regarding $\lambda$-perfect maps will be…
We show how our recent results on compositions of d.c. functions (and mappings) imply positive results on extensions of d.c. functions (and mappings). Examples answering two natural relevant questions are presented. Two further theorems,…
We characterize the Zariski topologies over an algebraically closed field in terms of general dimension-theoretic properties. Some applications are given to complex manifold and to strongly minimal sets.
We use a recent theorem of N. A. Karpenko and A. S. Merkurjev to settle several questions in the theory of essential dimension.
We determine a strong form of the decomposition theorem for proper toric maps over finite fields.
Extension dimension is characterized in terms of $\omega$-maps. We apply this result to prove that extension dimension is preserved by refinable maps between metrizable spaces. It is also shown that refinable maps preserve some…
In this paper,based on the available mathematical works on geometry and topology of hyperbolic manifolds and discrete groups, some results of Freedman et al (hep-th/9804058) are reproduced and broadly generalized. Among many new results the…
We strengthen some estimations of the local and global {\L}ojasiewicz exponent for polynomial mappings on closed semialgebraic sets obtained by K.Kurdyka, S.Spodzieja and A.Szlachci\'nska.
Let $M$ be a complete metric $ANR$-space such that for any metric compactum $K$ the function space $C(K,M)$ contains a dense set of Bing (resp., Krasinkiewicz) maps. It is shown that $M$ has the following property: If $f\colon X\to Y$ is a…
There is a complex conformal transformation, which maps the $D$ - dimensional real Minkowski space on a bounded set in the $D$ - dimensional complex vector space. It generalizes the Cayley map from $D=1$ dimensions to higher space-time…
Some generalizations of the classical Hurewicz formula are obtained for extension dimension and C-spaces.
We extend the definition of quasi-finite complexes by considering not necessarily countable complexes. We provide a characterization of quasi-finite complexes in terms of L-invertible maps and dimensional properties of compactifications.…
We extend the theory of separately holomorphic mappings between complex analytic spaces. Our method is based on Poletsky theory of discs, Rosay Theorem on holomorphic discs and our recent joint-work with Pflug on cross theorems in dimension…
Hurewicz's dimension-raising theorem states that for every n-to-1 map f : X \to Y, dim Y =< dim X + n holds. In this paper we introduce a new notion of finite-to-one like map in a large scale setting. Using this notion we formulate a…
We discuss solutions of several questions concerning the geometry of conformal planes.
An extension of dimensional regularization to the case of compact dimensions is presented. The procedure preserves the Kaluza-Klein tower structure, but has a regulator specific to the compact dimension. Possible 5 and 4 dimensional…
In this paper we give an alternative proof and a refinement of a recent result of S.D.Iliadis concerning isometrically containing mappings. We address also a recent result by A.I.Oblakova.
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.