Related papers: Universally complete spaces of continuous function…

We develop a generalized covering space theory for a class of uniform spaces called coverable spaces. Coverable spaces include all geodesic metric spaces, connected and locally pathwise connected compact topological spaces, in particular…

We determine the class of finite T_0-spaces allowing for a universal coefficient theorem computing equivariant KK-theory by filtrated K-theory.

We prove that for every $T_0$ space $X$, there is a well-filtered space $W(X)$ and a continuous mapping $\eta_X: X\lra W(X)$ such that for any well-filtered space $Y$ and any continuous mapping $f: X\lra Y$ there is a unique continuous…

Let $\mathcal C$ be a class of topological semigroups. A semigroup $X$ is called $absolutely$ $\mathcal C$-$closed$ if for any homomorphism $h:X\to Y$ to a topological semigroup $Y\in\mathcal C$, the image $h[X]$ is closed in $Y$. Let…

We prove that every vertically nearly separately continuous function defined on a product of a strong PP-space and a topological space and with values in a strongly $\sigma$-metrizable space with a special stratification, is a pointwise…

Consider a self-similar space X. A typical situation is that X looks like several copies of itself glued to several copies of another space Y, and Y looks like several copies of itself glued to several copies of X, or the same kind of thing…

We consider the classical Skorokhod space $D[0,1]$ and the space of continuous functions $C[0,1]$ equipped with the standard Skorokhod distance $\rho$. It is well known that neither $(D[0,1],\rho)$ nor $(C[0,1],\rho)$ is complete. We…

Let be F a family of curves in the unit disc. We show that the set of all functions f holomorphic on the unit disc, which satisfy the following condition, is G-delta and dense in the space of all functions holomorphic on the unit disc: For…

This article is a fundamental study in computable analysis. In the framework of Type-2 effectivity, TTE, we investigate computability aspects on finite and infinite products of effective topological spaces. For obtaining uniform results we…

We say that a metrizable space $M$ is a Krasinkiewicz space if any map from a metrizable compactum $X$ into $M$ can be approximated by Krasinkiewicz maps (a map $g\colon X\to M$ is Krasinkiewicz provided every continuum in $X$ is either…

If G is a Polish group, then there is a Polish G-space X which is universal among Polish G-spaces with respect to continuous G-embeddings.

For a nonempty compact subset $\sigma$ in the plane, the space $AC(\sigma)$ is the closure of the space of complex polynomials in two real variables under a particular variation norm. In the classical setting, $AC[0,1]$ contains several…

The goal of this paper is to present a complete characterisation of points of order continuity in abstract Ces\`aro function spaces $CX$ for $X$ being a symmetric function space. Under some additional assumptions mentioned result takes the…

The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, especially their properties from a chronological point of view. Each our spacetime is stationary cylindrically symmetric and it is filled…

Let $X$ be metrizable, $Y$ be perfectly normal and suppose that there exists a uniformly continuous surjection $T: C_{p}(X) \to C_{p}(Y)$ (resp., $T: C_{p}^*(X) \to C_{p}^*(Y)$), where $C_{p}(X)$ (resp., $C_{p}^*(X)$) denotes the space of…

We are considering typed hierarchies of total, continuous functionals using complete, separable metric spaces at the base types. We pay special attention to the so called Urysohn space constructed by P. Urysohn. One of the properties of the…

This paper collects results and open problems concerning several classes of functions that generalize uniform continuity in various ways, including those metric spaces (generalizing Atsuji spaces) where all continuous functions have the…

We extend in this paper several results of E. Kirchberg, S. Wassermann and the author dealing with continuous fields of C*--algebras to the semi-continuous case. We provide a new characterisation of separable lower semi-continuity…

This paper presents two general criteria to determine spaceability results in the complements of unions of subspaces. The first criterion applies to countable unions of subspaces under specific conditions and is closely related to the…

We give a new scale of completeness conditions for exponential systems in two types of functional spaces on subsets of the complex plane. The first is the Banach spaces of functions that are continuous on a compact and simultaneously…