相关论文: The dimension of hyperspaces of non-metrizable con…

Let $X$ be a continuum and let $C(X)$ denote the hyperspace of subcontinua of $X$, endowed with the Hausdorff metric. For $p\in X$, define the hyperspace $C(p,X)=\{A\in C(X):p\in A\}$ as a subspace of $C(X)$. In this paper we introduced the…

We prove that: 1. If a Hausdorff M-space is a continuous closed image of a submetrizable space, then it is metrizable. 2. A dense-in-itself open-closed image of a submetrizable space is submetrizable if and only if it is functionally…

We prove two theorems which allow one to recognize indecomposable subcontinua of closed surfaces without boundary. If $X$ is a subcontinuum of a closed surface $S$, we call the components of $S \setminus X$ the complementary domains of $X$.…

Let X be a compact Hausdorff space. Then the radius of comparison rc ( C (X)) is related to the covering dimension dim (X) by rc ( C (X)) \geq [ dim (X) - 7 ] / 2. Except for the additive constant, this improves a result of Elliott and Niu,…

Given a continuum $X$, let $C(X)$ denote the hyperspace of all subcontinua of $X$. In this paper we study the Vietoris hyperspace $NC^{*}(X)=\{ A \in C(X):X\setminus A\text{ is connected}\}$ when $X$ is a finite graph or a dendrite; in…

A metric continuum $X$ is indecomposable if it cannot be put as the union of two of its proper subcontinua. A subset $R$ of $X$ is said to be continuumwise connected provided that for each pair of points $p,q\in R$, there exists a…

In a previuos paper the author asked if there exists a one-dimensional space $X$ that is not almost zero-dimensional, such that the dimension of the hyperspace of compact subsets of $X$ is one-dimensional. In this short note we give…

Any unital separable continuous C(X)-algebra with properly infinite fibres is properly infinite as soon as the compact Hausdorff space X has finite topological dimension. We study conditions under which this is still the case in the…

We show that if $(X,d)$ is a metric space which admits a consistent convex geodesic bicombing, then we can construct a conical bicombing on $CB(X)$, the hyperspace of nonempty, closed, bounded, and convex subsets of $X$ (with the Hausdorff…

It is shown that the Hochschild Cohomological dimension of an associative algebra is not an upper-semi continuous function, showing the semi-continuity theorem is no longer valid for non-commutative algebras. A family of $\mathbb{C}$…

We characterize metric spaces $X$ whose hyperspaces $2^X$ or $Bd(X)$ of non-empty closed (bounded) subsets, endowed with the Hausdorff metric, are absolute [neighborhood] retracts.

Let $X$ be a nondegenerate Peano unicoherent continuum. The family $CB(X)$ of proper subcontinua of $X$ with connected boundaries is a $G_\delta$-subset of the hyperspace $C(X)$ of all subcontinua of $X$. If every nonempty open subset of…

Any unital separable continuous C(X)-algebra with properly infinite fibres is properly infinite as soon as the compact Hausdorff space X has finite topolog-ical dimension. We study conditions under which this is still the case if the…

The 2-locality problem of diameter-preserving maps between C(X)-spaces is addressed in this paper. For any compact Hausdorff space X with at least three points, we give an example of a 2-local diameter-preserving map on C(X) which is not…

Given a continuum $X$ and $p\in X$, we will consider the hyperspace $C(p,X)$ of all subcontinua of $X$ containing $p$. Given a family of continua $\mathcal{C}$, a continuum $X\in\mathcal{C}$ and $p\in X$, we say that $(X,p)$ has unique…

A Hausdorff topological space X is van der Waerden if for every sequence (x_n)_n in X there is a converging subsequence (x_n)_{n in A} where subset A of omega contains arithmetic progressions of all finite lengths. A Hausdorff topological…

We prove that each non-metrizable sequential rectifiable space $X$ of countable $cs^*$-character contains a clopen rectifiable submetrizable $k_\omega$-subspace $H$ and admits an open disjoint cover by subspaces homeomorphic to clopen…

A topological space $X$ is called hereditarily supercompact if each closed subspace of X is supercompact. By a combined result of Bula, Nikiel, Tuncali, Tymchatyn, and Rudin, each monotonically normal compact Hausdorff space is hereditarily…

We shall prove that if X, Y are compact metrizable spaces of positive dimension and h: X x Y --> X is a continuous map with zero-dimensional fibers then X contains a non-trivial continuum without one-dimensional subsets; in particular X is…

We study some forward invariant sets appearing in the dynamics of the exponential family. We prove that the Hausdorff dimension of the sets under consideration is not larger than $1$. This allows us to prove, as a consequence, a result for…