相关论文: On imbedding of closed 2-dimensional disks into $R…

A new approach to Nori's weak Lefschetz theorem is described. The new approach, which involves the dbar-method, avoids moving arguments and gives much stronger results. In particular, it is proved that if X and Y are connected smooth…

Surfaces of finite geometric type are complete, immersed into the tree-dimensional Euclidean space with finite total curvature and Gauss map extending to an oriented compact surface as a smooth branched covering map over the unit sphere of…

In this paper we are interested in computability aspects of subshifts and in particular Turing degrees of 2-dimensional SFTs (i.e. tilings). To be more precise, we prove that given any \pizu subset $P$ of $\{0,1\}^\NN$ there is a SFT $X$…

Using quasiconformal mappings, we prove that any Riemann surface of finite connectivity and finite genus is conformally equivalent to an intrinsic circle domain U in a compact Riemann surface S. This means that each connected component B of…

The partition number $\pi(K)$ of a simplicial complex $K\subset 2^{[m]}$ is the minimum integer $\nu$ such that for each partition $A_1\uplus\ldots\uplus A_\nu = [m]$ of $[m]$ at least one of the sets $A_i$ is in $K$. A complex $K$ is…

We show that if $f\colon I\to I$ is piecewise monotone, post-critically finite, and locally eventually onto, then for every point $x\in X=\underleftarrow{\lim}(I,f)$ there exists a planar embedding of $X$ such that $x$ is accessible. In…

A compact space $X$ is said to be minimal if there exists a map $f:X\to X$ such that the forward orbit of any point is dense in $X$. We consider rigid minimal spaces, motivated by recent results of Downarowicz, Snoha, and Tywoniuk [J. Dyn.…

Assume that $\mathcal{P}$ is a topological property of a space $X$, then we say that $X$ is {\it dense-$\mathcal{P}$} if each dense subset of $X$ has the property $\mathcal{P}$. In this paper, we mainly discuss dense subsets of a space $X$,…

Let $X$ be a compact metric space and let $f:X\rightarrow X$ be a homeomorphism on $X$. We show that if $f$ is both pointwise recurrent and expansive, then the dynamical system $(X, f)$ is topologically conjugate to a subshift of some…

We show that if a separable space X has a meager open subset containing a copy of the Cantor set 2^\omega, then X has $\frak{c}$ types of countable dense subsets. We suggest a generalization of the \lambda-set for non-separable spaces. Let…

Let $\{U_t \}_{t \in {\mathbb D}}$ be a family of topological disks on the Riemann sphere containing the origin 0 whose boundaries undergo a holomorphic motion over the unit disk $\mathbb D$. We study the question of when there exists a…

For a simply connected domain $G$, let $\partial_{a}G$ be the set of accessible points in $\partial G$ and let $\partial_{n} G=\partial G-\partial_{a}G$. A point $a\in\partial G$ is called semi-unreachable if there is a crosscut $J$ of $G$…

We consider a self-homeomorphism h of some surface S. A subset F of the fixed point set of h is said to be unlinked if there is an isotopy from the identity to h that fixes every point of F. With Le Calvez' transverse foliations theory in…

It is known that if a compact metric space X admits a minimal expansive homeomorphism then X is totally disconnected. In this note we give a short proof of this result and we analyze its extension to expansive flows.

We consider a surface $M$ immersed in $\mathbb{R}^3$ with induced metric $g=\psi\delta_2$ where $\delta_2$ is the two dimensional Euclidean metric. We then construct a system of partial differential equations that constrain $M$ to lift to a…

We show that a homeomorphism of a semi-locally connected compact metric space is equicontinuous if and only if the distance between the iterates of a given point and a given subcontinuum (not containing that point) is bounded away from…

Let ${\mathscr P}$ be a topological property. We say that a space $X$ is ${\mathscr P}$-connected if there exists no pair $C$ and $D$ of disjoint cozero-sets of $X$ with non-${\mathscr P}$ closure such that the remainder $X\backslash(C\cup…

Let $\mathcal C$ be a class of topological semigroups. A semigroup $X$ is $injectively$ $\mathcal C$-$closed$ if $X$ is closed in each topological semigroup $Y\in\mathcal C$ containing $X$ as a subsemigroup. Let $\mathsf{T_{\!2}S}$ (resp.…

Let M be a closed 5-manifold of pinched curvature 0<\delta\le \text{sec}_M\le 1. We prove that M is homeomorphic to a spherical space form if M satisfies one of the following conditions: (i) \delta =1/4 and the fundamental group is a…

We prove various reconstruction theorems about open subsets of normed spaces. E.g. if the uniformly continuous homeomorphism groups of two such sets are isomorphic, then this isomorphism is induced by a uniformly continuous homeomorphism…