Related papers: Uniform homeomorphisms between spheres induced by …

In this paper, we prove first that the space of minimal sets of any homeomorphisms $f:X\to X$ of a regular curve $X$ is closed in the hyperspace $2^X$ of closed subsets of $X$ endowed with the Hausdorff metric, and the non-wandering set…

We consider the problem of whether there is a sequence of homeomorphisms $(F_k)_k$ between the unit spheres of the $k$-dimensional Banach spaces $\ell_\infty^k$ and $\ell_1^k$ which is also equi-uniformly continuous. We prove that this…

In this paper,\ the authors define a space with an uniform base at non-isolated points, give some characterizations of images of metric spaces by boundary-compact maps, and study certain relationship among spaces with special base…

For a finite simplicial complex K and a CW-pair (X,A), there is an associated CW-complex Z_K(X,A), known as a polyhedral product. We apply discrete Morse theory to a particular CW-structure on the n-sphere moment-angle complexes Z_K(D^{n},…

We show that if $(\ell_{\phi_0}, \ell_{\phi_1})$ is a couple of suitable Orlicz sequence spaces then the corresponding Rochberg derived spaces of all orders associated to the complex interpolation method are Fenchel-Orlicz spaces. In…

Given a convergent sequence of nodes we present a one-dimensional-holomorphic-function version of the Newton interpolation method of polynomials. It also generalises the Taylor and the Laurent formula. In other words, we present an…

We prove that for every Hausdorff space X and any uniform quadra space (Y,U) the topology on C(X,Y) induced by the uniformity U| of uniform convergence on the saturation family L coincides with the set-open topology on C(X,Y). In…

It is shown that the first and second homotopy groups of the $\eta$-inverted sphere spectrum over a field of characteristic not two are zero. A cell presentation of higher Witt theory is given as well, at least over the complex numbers.

In 1967, Peetre proposed to give a precise description of the real interpolation space for Besov hierarchical spaces $l^{s,q}(A)$. In 1974, Cwikel proved that the Lions-Peetre formula for $(l^{q_0}(A_0), l^{q_1}(A_1))_{\theta,r}$ have no…

We introduce the concept of a standard form for two embedded maximal sphere systems in the doubled handlebody, and we prove an existence and uniqueness result. In particular, we show that pairs of maximal sphere systems in the doubled…

The notions of discrete conformality on triangle meshes have rich mathematical theories and wide applications. The related notions of discrete uniformizations on triangle meshes, suggest efficient methods for computing the uniformizations…

Let X be a connected topological space admitting a universal cover. Let a be a degree one cohomology class on X. We define and study a two-cocycle on a group acting on X by homeomorphisms preserving the class a. We use this cocycle to…

To every closed subset $X$ of a symplectic manifold $(M,\omega)$ we associate a natural group of Hamiltonian diffeomorphisms $Ham(X,\omega)$. We equip this group with a semi-norm $\Vert\cdot\Vert^{X,\omega}$, generalizing the Hofer norm. We…

This paper conglomerates our findings on the space $C(X)$ of all real valued continuous functions, under different generalizations of the topology of uniform convergence and the $m$-topology. The paper begins with answering all the…

Let $M$ be an open Riemann surface and $n\ge 3$ be an integer. We prove that on any closed discrete subset of $M$ one can prescribe the values of a conformal minimal immersion $M\to\mathbb{R}^n$. Our result also ensures jet-interpolation of…

Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point…

We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…

We define $\partial$-biLipschitz homeomorphisms between uniform metric spaces and show that these maps are always quasim\"obius. We also show that a homeomorphism being $\partial$-biLipschitz is equivalent to the map biLipschitz in the…

We denote by $\Hp$ the Hilbert space of ordinary Dirichlet series with square-summable coefficients. The main result is that a bounded sequence of points in the half-plane $\sigma >1/2$ is an interpolating sequence for $\Hp$ if and only if…

We prove that a compactly supported homeomorphism of a smooth manifold of dimension greater or equal to 5 can be approximated uniformly by compactly supported diffeomorphisms if and only if it is isotopic to a diffeomorphism. If the given…