Related papers: Completeness in quasi-pseudometric spaces
This paper has two goals: to present some new results that are necessary for further study and applications of quasi-linear functionals, and, by combining known and new results, to serve as a convenient single source for anyone interested…
Nearly three decades from his celebrated result, we study a modern refinement and strengthening of Kopperman's full metrisabilty of all topological spaces. Within this new theory of \emph{V-spaces}, developed by Flagg and Weiss, we…
We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space equipped with a doubling measure supporting a p-Poincar\'e inequality with 1<p<\infty, and connect them to the Sobolev theory in R^n. In…
We prove a general quantitative theorem on the asymptotic behavior of stochastic quasi-Fej\'er monotone sequences in a broad metric context. Concretely, our result explicitly constructs a rate of convergence for such process, both in mean…
Our main result states that, given a finite-dimensional vector space $E$, the pseudometric defined in the set of continuous quasinorms $\mathcal{Q}_0=\{\|\cdot\|:E\to\mathbb{R}\}$ as $$d(\|\cdot\|_X,\|\cdot\|_Y)=\min\{\mu:\|\cdot\|_X…
The topic is the history of the concepts of equivalence relation, Cauchy sequence, and metric space. The thesis is that disused definitions of these notions could profitably be revived.
We show that a homeomorphism of Euclidean space is quasiconformal if and only if at each point there exists a sequence of uncentered open sets with bounded eccentricity shrinking to that point whose images also have bounded eccentricity.…
The first aim of this study is to define soft sequential compact metric spaces and to investigate some important theorems on soft sequential compact metric space. Second is to introduce net and totally bounded soft metric space and study…
We survey the recent developments in the theory of quasireg- ular mappings in metric spaces. In particular, we study the geometric porosity of the branch set of quasiregular mappings in general metric measure spaces, and then, introduce the…
We clarify and discuss a misunderstanding between uniform completeness and metric completeness, that has appeared in the literature in a study on the Alexandrov topology for a spacetime.
We prove versions of Ekeland, Takahashi and Caristi principles in preordered quasi-metric spaces, the equivalence between these principles, as well as their equivalence to some completeness results for the underlying quasi-metric space.…
We consider several quantities related to weak sequential completeness of a Banach space and prove some of their properties in general and in $L$-embedded Banach spaces, improving in particular an inequality of G. Godefroy, N. Kalton and D.…
The purpose of this paper is to investigate the stationary dense operators and their connection to distribution semigroups and abstract Cauchy problem in sequentially complete spaces.
The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the…
The famous Banach Contraction Principle holds in complete metric spaces, but completeness is not a necessary condition -- there are incomplete metric spaces on which every contraction has a fixed point. The aim of this paper is to present…
We initiate the rigorous study of classification in quasi-metric spaces. These are point sets endowed with a distance function that is non-negative and also satisfies the triangle inequality, but is asymmetric. We develop and refine a…
In a recent paper, two multi-representations for the measurable sets in a computable measure space have been introduced, which prove to be topologically complete w.r.t. certain topological properties. In this contribution, we show them…
This paper is devoted to the study of the relatively compact sets in Quasi-Banach function spaces, providing an important improvement of the known results. As an application, we take the final step in establishing a relative compactness…
Square contingency tables are traditionally analyzed with a focus on the symmetric structure of the corresponding probability tables. We view probability tables as elements of a simplex equipped with the Aitchison geometry. This perspective…
In this paper we present different ways to parametrize subsets of the space of valuations on $K[x]$ extending a given valuation on $K$. We discuss the methods using pseudo-Cauchy sequences and approximation types. The method presented here…