Related papers: Separating Homeomorphisms
In this paper we show that the group of automorphisms of a non-recurrent tent map inverse limit is very simple by demonstrating that every homeomorphism of such a space is isotopic to a power of the induced shift homeomorphism.
We show that the endomorphisms of a compact connected group that extend to endomorphisms of every compact overgroup are precisely the trivial one and the inner automorphisms; this is an analogue, for compact connected groups, of results due…
In this paper we further explore the L-shadowing property defined in [17] for dynamical systems on compact spaces. We prove that structurally stable diffeomorphisms and some pseudo-Anosov diffeomorphisms of the two-dimensional sphere…
We proof here the existence of a topological thick and thin decomposition of any closed definable thick isolated singularity germ in the spirit of the recently discovered metric thick and thin decomposition of complex normal surface…
A topological space is nonseparably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected first countable space is the image of a nonseparably connected complete metric space…
We define the notions of unilateral metric derivatives and ``metric derived numbers'' in analogy with Dini derivatives (also referred to as ``derived numbers'') and establish their basic properties. We also prove that the set of points…
We show that the group of type-preserving automorphisms of any irreducible semi-regular thick right-angled building is abstractly simple. When the building is locally finite, this gives a large family of compactly generated (abstractly)…
For a compact space $K$ we denote by $C_w(K)$ ($C_p(K)$) the space of continuous real-valued functions on $K$ endowed with the weak (pointwise) topology. In this paper we address the following basic question which seems to be open: Suppose…
For an $\alpha$-expansive homeomorphism of a compact space we give an elementary proof of the following well-known result in topological dynamics: A sufficient condition for the homeomorphism to have the shadowing property is that it has…
We study the asymptotic behavior of the homotopy groups of simply connected finite $p$-local complexes, and define a space to be locally hyperbolic if its homotopy groups have exponential growth. Under some certain conditions related to the…
This paper discusses the dynamics of continuum-wise hyperbolic surface homeomorphisms. We prove that $cw_F$-hyperbolic surface homeomorphisms containing only a finite set of spines are $cw_2$-hyperbolic. In the case of $cw_3$-hyperbolic…
On a smooth connected manifold, we consider all possible locally elliptic and locally bounded measurable coefficient Riemannian metrics called rough Riemannian metrics. We equip this set with an extended metric which is connected if and…
In this article we consider several forms of expansivity. We introduce two new definitions related with topological dimension. We study the topology of local stable sets under cw-expansive surface homeomorphisms and expansive homeomorphisms…
In this work, we study the concept of self-overlapping permutations, which is related to the larger study of consecutive patterns in permutations. We show that this concept admits a simple and clear geometrical meaning, and prove that a…
We analytically compute asymptotic expansions of a 1-dimensional sub-manifold of stable and unstable manifolds in a 4-dimensional symplectic mapping by using the method called asymptotic expansions beyond all orders. This method enables us…
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…
Let $f$ be an $R$-closed homeomorphism on a connected orientable closed surface $M$. In this paper, we show that If $M$ has genus more than one, then each minimal set is either a periodic orbit or an extension of a Cantor set. If $M =…
For two not necessarily commutative topological groups G and T, let H(G,T) denote the space of all continuous homomorphisms from G to T with the compact-open topology. We prove that if G is metrizable and T is compact then H(G,T) is a…
The complexity quasi-metric of Schellekens is a topological framework in which the asymmetry of computational comparisons -- ``$A$ is at most as fast as $B$'' carrying different information than ``$B$ is at most as slow as $A$'' -- is built…
The Urysohn universal metric space U is characterized up to isometry by the following properties: (1) U is complete and separable; (2) U contains an isometric copy of every separable metric space; (3) every isometry between two finite…