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

Continuous functions on the unit interval are relatively tame from the logical and computational point of view. A similar behaviour is exhibited by continuous functions on compact metric spaces equipped with a countable dense subset. It is…

Divisible convex sets have long been important in the study of Hilbert geometries. When a divisible convex set is an ellipsoid, the Hilbert geometry it induces is the hyperbolic space. In general, strictly convex divisible domains exhibit…

Let $X$ be a Hausdorff compact space and $C(X)$ be the algebra of all continuous complex-valued functions on $X$, endowed with the supremum norm. We say that $C(X)$ is (approximately) $n$-th root closed if any function from $C(X)$ is…

Results on the upper and lower semicontinuity of functionals defined on spaces of convex and more general functions are established. In particular, the following result is obtained. Let $\phi(v; \cdot)$ be the density of the absolutely…

The bounded localization $\beta_b$ of a locally convex topology $\beta$ is defined as the finest locally convex topology agreeing with $\beta$ on all bounded sets. We show that the strict topology on the multiplier algebra of a bornological…

We introduce the notion of compactifiable classes -- these are classes of metrizable compact spaces that can be up to homeomorphic copies ``disjointly combined'' into one metrizable compact space. This is witnessed by so-called compact…

A topological space is $Suslin$ ($Lusin$) if it is a continuous (and bijective) image of a Polish space. For a Tychonoff space $X$ let $C_p(X)$, $C_k(X)$ and $C_{{\downarrow}F}(X)$ be the space of continuous real-valued functions on $X$,…

In this paper we obtain results indicating that fine shape is tractable and "not too strong" even in the non-locally compact case, and can be used to better understand infinite-dimensional metrizable spaces and their homology theories. We…

In this paper we study connections between Besov spaces of functions on a compact metric space $Z$, equipped with a doubling measure, and the Newton--Sobolev space of functions on a uniform domain $X_\varepsilon$. This uniform domain is…

To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a locally compact space $\Si$ endowed with a Radon measure, one associates a coorbit theory converting spaces of functions on $\Si$ in spaces of vectors comparable…

Using classical results of infinite-dimensional geometry, we show that the isometry group of the Urysohn space, endowed with its usual Polish group topology, is homeomorphic to the separable Hilbert space. The proof is basedon a lemma about…

We show that $C(X)$ admits an equivalent pointwise lower semicontinuous locally uniformly rotund norm provided $X$ is Fedorchuk compact of spectral height 3. In other words $X$ admits a fully closed map $f$ onto a metric compact $Y$ such…

We investigate multipliers on the space of holomorphic functions $H(\Omega)$, where $\Omega \subset \mathbb{C}^n$ is an open set. For Runge domains, we characterize these multipliers as convolutions with analytic functionals. Additionally,…

This paper studies topological duals of Banach function spaces (BFS). We assume a finite measure but our arguments extend to general locally convex function spaces whose topology is generated by seminorms that satisfy the usual BFS axioms.…

The main aim of the paper is to introduce the concept of metric duality in the category of topological Abelian groups that extends the classical notion of duality for normed vector spaces and behaves quite nicely for LCA groups (equipped…

For a metrizable space $X$ of density $\kappa$, let $PM(X)$ be the space of continuous bounded pseudometrics on $X$ endowed with the uniform convergence topology. In this paper, its topology shall be classified as follows: (i) If $X$ is…

We study some non-local functionals on the Sobolev space $W^{1,p}_0(\Omega)$ involving a double integral on $\Omega\times\Omega$ with respect to a measure $\mu$. We introduce a suitable notion of convergence of measures on product spaces…

We consider the isometry group of the infinite dimensional separable hyperbolic space with its Polish topology. This topology is given by the pointwise convergence. For non-locally compact Polish groups, some striking phenomena like…

A homeomorphism on a compact metric space is said hyper-expansive if every pair of different compact sets are separated by the homeomorphism in the Hausdorff metric. We characterize such dynamics as those with a finite number of orbits and…

In this article, we give some fixed point results in left $K$-complete quasi-pseudometric type spaces for self-mappings that are $(C_\alpha,C_\beta)$-admissible.