Related papers: Uniform covers at non-isolated points
A topological space $X$ is defined to have an $\omega^\omega$-base if at each point $x\in X$ the space $X$ has a neighborhood base $(U_\alpha[x])_{\alpha\in\omega^\omega}$ such that $U_\beta[x]\subset U_\alpha[x]$ for all $\alpha\le\beta$…
In this paper we will study the representations of isomorphisms between bases of topological spaces. It turns out that the perfect setting for this study is that of regular open subsets of complete metric spaces, but we have achieved some…
Let $X$ be an irreducible, reduced complex projective hypersurface of degree $d$. A point $P$ not contained in $X$ is called uniform if the monodromy group of the projection of $X$ from $P$ is isomorphic to the symmetric group $S_d$. We…
We show that if $K$ is a compact metrizable space with finitely many accumulation points, then the closed unit ball of $C(K)$ is a plastic metric space, which means that any non-expansive bijection from $B_{C(K)}$ onto itself is in fact an…
A convex subset X of a linear topological space is called compactly convex if there is a continuous compact-valued map $\Phi:X\to exp(X)$ such that $[x,y]\subset\Phi(x)\cup \Phi(y)$ for all $x,y\in X$. We prove that each convex subset of…
In this survey we present a generalization of the notion of metric space and some applications to discrete structures as graphs, ordered sets and transition systems. Results in that direction started in the middle eighties based on the…
We introduce and study the operation, called dense amalgam, which to any tuple X_1,...,X_k of non-empty compact metric spaces associates some disconnected perfect compact metric space, denoted $\widetilde\sqcup(X_1,...,X_k)$, in which there…
We give a simple conceptual proof of the consistency of a test for multivariate uniformity in a bounded set $K \subset \mathbb{R}^d$ that is based on the maximal spacing generated by i.i.d. points $X_1, \ldots,X_n$ in $K$, i.e., the volume…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
Let $X$ be a metrizable space and ${\rm Comp}(X)$ be the hyperspace consisting of non-empty compact subsets of $X$ endowed with the Vietoris topology. In this paper, we give a necessary and sufficient condition on $X$ for ${\rm Comp}(X)$ to…
This study focuses on defining normal and strictly convex structures within Menger cone PM-space. It also presents a shared fixed point theorem for the existence of two self-mappings constructed on a strictly convex probabilistic cone…
An open (resp., closed) subset A of a topological space (X, T ) is called C-open (resp., C-closed) set if cl(A) \ A (resp., A \ int(A)) is a countable set. This paper aims to present the concept of C-open and C-closed sets. We first…
We generalize the van Kampen theorem for unions of non-connected spaces, due to R. Brown and A. R. Salleh, to the context where families of subspaces of a space B are replaced by a locally sectionable map to B.
Generalizing the case of an infinite discrete metric space of finite diameter, we say that a discrete metric space $(X,d)$ is a Kuiper space, if the group of invertible elements of its uniform Roe algebra is norm-contractible. Various…
Given uniformly homeomorphic metric spaces $X$ and $Y$, it is proved that the hyperspaces $C(X)$ and $C(Y)$ are uniformly homeomorphic, where $C(X)$ denotes the collection of all nonempty closed subsets of $X$, and is endowed with Hausdorff…
In this article we introduce and study a natural form of expansivity, that we call \textit{metric-independent expansiveness}, for group actions on metrizable spaces. This notion means \textit{expansive with respect to every compatible…
Mutually Unbiased Bases (MUBs) are closely connected with quantum physics, and the structure has a rich mathematical background. We provide equivalent criteria for extending a set of MUBs for $C^n$ by studying real points of a certain…
We prove that the space of free boundary CMC surfaces of bounded topology, bounded area and bounded boundary length is compact in the $C^k$ graphical sense away from a finite set of points. This is a CMC version of a result for minimal…
In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.
The aim of this paper is to prove a fixed point theorem on a generalised cone metric spaces for maps satisfying general contractive type conditions.