Related papers: About the space of continuous functions with open …

This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…

For $X$, $Y$, $Z$ and $W$ compact metric spaces, consider two uniformly contractive IFS $\{\tau_x: Z\to Z,\, x\in x\}$ and $\{\tau_y:W\to W,\, y\in Y\}$. For a fixed $\alpha \in \mathcal{P}(X)$ with $supp(\alpha)=X$ we define the entropy of…

Let $\Gamma$ be a Polish space and let $K$ be a separable and pointwise compact set of real-valued functions on $\Gamma$. It is shown that if each function in $K$ has only countably many discontinuities then $C(K)$ may be equipped with a…

This paper employs techniques from metric geometry and optimal transport theory to address questions related to the analysis of functional data on metric or metric-measure spaces, which we refer to as fields. Formally, fields are viewed as…

Let $\{P_t\}_{t>0}$ be the Dunkl-Poisson semigroup associated with a root system $R\subset \mathbb R^N$ and a multiplicity function $k\geq 0$. Analogously to the classical theory, we say that a bounded measurable function $f$ defined on…

It is formulated conditions on functions $Q(x)$ and boundaries of domains under which every $Q$-homeomorphism admits continuous or homeomorphic extension to the boundary in metric spaces with measures.

The following is an open problem in topology: Determine whether the Stone-\v{C}ech compactification of a widely-connected space is necessarily an indecomposable continuum. Herein we describe properties of $X$ that are necessary and…

Let $W$ be a domain in a connected complex manifold $M$ and $w_0\in W$. Let ${\mathcal A}_{w_0}(W,M)$ be the space of all continuous mappings of a closed unit disk $\overline D$ into $M$ that are holomorphic on the interior of $\overline…

In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that…

This article reviews a generous sampling of both classical and more recent results on the interplay between measurable and topological dynamics. In the first part we have surveyed the strong analogies between ergodic theory and topological…

In this note we prove that a regular continuous open image of the Sorgenfrey line with an uncountable weight has a closed subspace that is homeomorphic to the Sorgenfrey line. As a corollary we deduce the theorem in the title.

We study homeomorphisms of compact metric spaces whose restriction to the nonwandering set has the pseudo-orbit tracing property. We prove that if there are positively expansive measures, then the topological entropy is positive. Some short…

An analogue of Brylinski's knot beta function is defined for a compactly supported (Schwartz) distribution $T$ on $d$-dimensional Euclidean space. This is a holomorphic function on a right half-plane. If $T$ is a (uniform) double-layer on a…

For separable metrizable spaces $X,Y$ and a metrizable topological group $Z$ by $S(X\times Y,Z)$ we denote the space of all separately continuous functions $f:X\times Y\to Z$ endowed with the topology of layer-wise uniform convergence,…

A classical theorem of Kuratowski says that every Baire one function on a G_\delta subspace of a Polish (= separable completely metrizable) space X can be extended to a Baire one function on X. Kechris and Louveau introduced a finer…

For every n, we construct a metric measure space that is doubling, satisfies a Poincare inequality in the sense of Heinonen-Koskela, has topological dimension n, and has a measurable tangent bundle of dimension 1.

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 discuss the following basic question which seems to be open: Let $K$…

We define metrics in space that are natural counterparts of the hyperbolic metric in plane domains, using the characterization of the hyperbolic metric due to Beardon and Pommerenke. We obtain inequalities for these metrics under…

Dimensional types of metric scattered spaces are investigated. Revised proofs of Mazurkiewicz-Sierpi\'nski and Knaster-Urbanik theorems are presented. Embeddable properties of countable metric spaces are generalized onto uncountable metric…

The main result is a submetric characterization of the class of Banach spaces admitting an equivalent norm with Rolewicz's property ($\beta$). As applications we prove that up to renorming, property ($\beta$) is stable under coarse…