Related papers: On stable Baire classes

The rigidity of the positive mass theorem states that the only complete asymptotically flat manifold of nonnegative scalar curvature and zero mass is Euclidean space. We prove a corresponding stability theorem for spaces that can be…

Let $B_{1}(\Omega, \mathbb R)$ be the first Baire class of real functions in the pluri-fine topology on an open set $\Omega \subseteq \mathbb C^{n}$ and let $H_{1}^{*}(\Omega, \mathbb R)$ be the first functional Lebesgue class of real…

The paper is devoted to the fixed point theory in four aspects: of contractions, nonexpansive mappings, generalized inward mappings, and of the tool theorems. The manuscript was written about ten years ago. At first Nadler's concept of…

We show that stable derivators, like stable model categories, admit Mayer-Vietoris sequences arising from cocartesian squares. Along the way we characterize homotopy exact squares, and give a detection result for colimiting diagrams in…

We show that the typical nonexpansive mapping on a small enough subset of a CAT($\kappa$)-space is a contraction in the sense of Rakotch. By typical we mean that the set of nonexpansive mapppings without this property is a $\sigma$-porous…

Let {\Lambda}\subsetR^{n}\timesR^{m} and k be a positive integer. Let f:R^{n}\rightarrowR^{m} be a locally bounded map such that for each ({\xi},{\eta})\in{\Lambda}, the derivatives D_{{\xi}}^{j}f(x):=|((d^{j})/(dt^{j}))f(x+t{\xi})|_{t=0},…

Let X be a real algebraic subset of R^n and M a smooth, closed manifold. We show that all continuous maps from M to X are homotopic (in X) to C^\infty maps. We apply this result to study characteristic classes of vector bundles associated…

In this paper we disprove the following conjectured generalization of the Contraction Mapping Theorem (due to J.D. Stein Jr.): Let X be a complete metric space and let F be a finite family of self-maps of X. Suppose there is a postive…

We prove that the mapping stack Map(Y,X) of topological stacks X and Y is again a topological stack if Y admits a compact groupoid presentation. If Y admits a locally compact groupoid presentation, we show that Map(Y,X) is a paratopological…

Locally stable maps $S^3\to\mathbb{R}^4$ are classified up to homotopy through locally stable maps. The equivalence class of a map $f$ is determined by three invariants: the isotopy class $\sigma(f)$ of its framed singularity link, the…

We show that if a non-degenerate PL map $f:N\to M$ lifts to a topological embedding in $M\times\mathbb R^k$ then it lifts to a PL embedding in there. We also show that if a stable smooth map $N^n\to M^m$, $m\ge n$, lifts to a topological…

In this paper, we have proved results similar to Tychonoff's Theorem on embedding a space of functions with the topology of pointwise convergence into the Tychonoff product of topological spaces, but applied to the function space $C(X,Y)$…

We give a new proof of Cartan's fixed point theorem using topological fixed point theory. For an odd dimensional, simply connected and complete manifold having non-positive curvature, we further prove that every isometry with finite order…

We show that the class of C*-algebras with stable rank greater than a given positive integer is axiomatizable in logic of metric structures. As a consequence we show that the stable rank is continuous with respect to forming ultrapowers of…

We define an algebro-geometric model for the space of rational maps from a smooth curve X to an algebraic group G, and show that this space is homologically contractible. As a consequence, we deduce that the moduli space Bun(G) of G-bundles…

Let G be a connected Lie group, G^d the underlying discrete group, and BG, BG^d their classifying spaces. Let R denote the radical of G. We show that all classes in the image of the canonical map in cohomology H^*(BG,R)->H^*(BG^d,R) are…

A topological space ${\mathcal X}$ is reversible iff each continuous bijection (condensation) $f: {\mathcal X} \rightarrow {\mathcal X}$ is a homeomorphism; weakly reversible iff whenever ${\mathcal Y}$ is a space and there are…

We define the notion of {\em classifying space} of a topological stack and show that every topological stack \X has a classifying space X which is a topological space well-defined up to weak homotopy equivalence. Under a certain…

We consider open sets of maps in a manifold $M$ exhibiting non-uniform expanding behaviour in some domain $S\subset M$. Assuming that there is a forward invariant region containing $S$ where each map has a unique SRB measure, we prove that…

A map $f: \ff^n \to \ff^n$ over a field $\ff$ is called affine if it is of the form $f(x)=Ax+b$, where the matrix $A \in \ff^{n\times n}$ is called the linear part of affine map and $b \in \ff^n$. The affine maps over $\ff=\rr$ or $\cc$ are…