Related papers: Hurewicz theorem for extension dimension

Let W be a projective variety of dimension n+1, L a free line bundle on W, X in $H^0(L^d)$ a hypersurface of degree d which is generic among those given by sums of monomials from $L$, and let $f : Y \to X$ be a generically finite map from a…

We prove an analogue of E. Levi's Continuity Principle for meromorphic mappings with values in arbitrary compact complex manifolds in place of the Riemann sphere $\cc\pp^1$. The result is achieved by introducing a new extension method for…

Let W be a finite reflection group acting orthogonally on R^n, P be the Chevalley polynomial mapping determined by an integrity basis of the algebra of W-invariant polynomials, and h be the highest degree of the coordinate polynomials in…

The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…

We prove the following generalization of the Cartwright-Littlewood fixed point theorem. Suppose $ h\colon~{\mathbb R}^{2}\to{\mathbb R}^{2} $ is an orientation preserving planar homeomorphism, and $ X $ is an acyclic continuum. Let $ C $ be…

By means of hypercyclic operator theory, we complement our previous results on hypercyclic holomorphic maps between complex Euclidean spaces having slow growth rates,by showing {\it abstract abundance} rather than {\it explicit existence}.…

Let $E \subseteq \mathbb{R}^n$ be a union of line segments and $F \subseteq \mathbb{R}^n$ the set obtained from $E$ by extending each line segment in $E$ to a full line. Keleti's line segment extension conjecture posits that the Hausdorff…

In this paper we develop a technique of constructing uni- formly continuous maps between function spaces Cp(X) endowed with the pointwise topology. We prove that if a space X is compact metrizable and strongly countable-dimensional, then…

For an oriented manifold $M$ whose dimension is less than $4$, we use the contractibility of certain complexes associated to its submanifolds to cut $M$ into simpler pieces in order to do local to global arguments. In particular, in these…

A space $Y$ is called an {\em extension} of a space $X$ if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {\em equivalent} if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence…

For any Tychonoff space $X$ let $D(X)$ be either the set $C(X)$ of all continuous functions on $X$ or the set $C^*(X)$ of all bounded continuous functions on $X$. When $D(X)$ is endowed with the point convergence topology, we write…

Let $Y_{1}, \ldots, Y_{q}$ be closed subschemes which are located in $\ell$-subgeneral position with index $\kappa$ in a complex projective variety $X$ of dimension $n.$ Let $A$ be an ample Cartier divisor on $X.$ We obtain that if a…

We study "canonical weight decompositions" slightly generalizing that defined by J. Wildeshaus. For an triangulated category $C$, any integer $n$, and a weight structure $w$ on $C$ a triangle $LM\to M\to RM\to LM[1]$, where $LM$ is of…

We give necessary and sufficient conditions for certain pushouts of topological spaces in the category of Cech's closure spaces to agree with their pushout in the category of topological spaces. We prove that in these two categories, the…

This paper constructs an h-model structure for diagrams of streams, locally preordered spaces. Along the way, the paper extends some classical characterizations of Hurewicz fibrations and closed Hurewicz cofibrations. The usual…

The forcing method is a powerful tool to prove the consistency of set-theoretic assertions relative to the consistency of the axioms of set theory. Laver's theorem and Bukovsk\'y's theorem assert that set-generic extensions of a given…

We show that even for subsets X of the real line which do not contain perfect sets, the Hurewicz property does not imply the property S1(Gamma,Gamma), asserting that for each countable family of open gamma-covers of X, there is a choice…

We present a method to compute the holonomic extension of a $D$-module from a Zariski open set in affine space to the whole space. A particular application is the localization of coherent $D$-modules which are holonomic on the complement of…

Helly's selection theorem provides a criterion for compactness of sets of single-variable functions with bounded pointwise variation. Fra{\v{n}}kov{\'a} has given a proper extension of Helly's theorem to the setting of single-variable…

In this paper we introduce a general notion of weak extension property for embeddings induced by a group actions. As an example, for the group H(M, m) of measure-preserving homeomorphisms of a noncompact manifold M, we deduce weak type…