Related papers: Positively expansive homeomorphisms of compact spa…

In this article we introduce and study a natural form of expansivity, that we call \textit{metric-independent expansiveness}, for group actions on metrizable spaces. This notion means \textit{expansive with respect to every compatible…

We show that if $K$ is a compact metrizable space with finitely many accumulation points, then the closed unit ball of $C(K)$ is a plastic metric space, which means that any non-expansive bijection from $B_{C(K)}$ onto itself is in fact an…

We revisit the definition of effective local compactness, and propose an approach that works for arbitrary countably-based spaces extending the previous work on computable metric spaces. We use this to show that effective local compactness…

We define the concept of continuum wise expansive for set-valued functions and prove that if a compact metric space admit a set-valued $cw$-expansive function then the topological entropy of $X$ is positive.} We also introduce the notion of…

In this paper we give a new, and shorter, proof of Huber's theorem which affirms that for a connected open Riemann surface endowed with a complete conformal Riemannian metric, if the negative part of its Gaussian curvature has finite mass,…

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.…

Consider a manifold with boundary, and such that the interior is equipped with a pseudo-Riemannian metric. We prove that, under mild asymptotic non-vanishing conditions on the scalar curvature, if the Levi-Civita connection of the interior…

We study the classification of spaces of continuous functions $C(K)$ under positive linear maps. For infinite countable compacta, we show that whenever $C(K)$ and $C(L)$ are isomorphic, there exists an isomorphism $T:C(K)\to C(L)$…

We define shadowable points for homeomorphism on metric spaces. In the compact case we will prove the following results: The set of shadowable points is invariant, possibly nonempty or noncompact. A homeomorphism has the pseudo-orbit…

We show that any space with a positive upper curvature bound has in a small neighborhood of any point a closely related metric with a negative upper curvature bound.

We prove that two finite-dimensional commutative algebras over an algebraically closed field are isomorphic if and only if they give rise to isomorphic representations of the category of finite sets and surjective maps.

In this note we study some properties of topological entropy for non-compact non-metrizable spaces. We prove that if a uniformly continuous self-map $f$ of a uniform space has topological shadowing property then the map $f$ has positive…

We characterize and describe the extensions of expansive and Anosov homeomorphisms on compact spaces. As an application we obtain a stability result for extensions of Anosov systems, and show a construction that embeds any expansive system…

We show that a linearly ordered topological space is initially \lambda-compact if and only if it is \lambda-bounded, that is, every set of cardinality $\leq \lambda$ has compact closure. As a consequence, every product of initially…

We prove that local stable/unstable sets of homeomorphisms of an infinite compact metric space satisfying the gluing-orbit property always contain compact and perfect subsets of the space. As a consequence, we prove that if a positively…

For a finite and positive measure space $(\Omega,\Sigma,\mu)$ and any weakly compact convex subset of $L\sp\infty(\Omega,\Sigma,mu)$, a fixed point theorem for a class of nonexpansive self-mappings is proved. An analogous result is obtained…

We call a dynamical system on a measurable metric space {\em measure-expansive} if the probability of two orbits remain close each other for all time is negligible (i.e. zero). We extend results of expansive systems on compact metric spaces…

We provide examples of non-locally compact geodesic Ptolemy metric spaces which are not uniquely geodesic. On the other hand, we show that locally compact, geodesic Ptolemy metric spaces are uniquely geodesic. Moreover, we prove that a…

The main result of this note essentially is that if the base and fibers of a compact fibration carry Hermitian metrics of positive holomorphic sectional curvature, then so does the total space of the fibration. The proof is based on the use…

Let $M$ be a compact manifold of dimension at least 2. If $M$ admits a minimal homeomorphism then $M$ admits a minimal noninvertible map.