相关论文: A remark on $\beta$-locally closed sets
Given a graph $G = (V,E)$, an $(\alpha, \beta)$-ruling set is a subset $S \subseteq V$ such that the distance between any two vertices in $S$ is at least $\alpha$, and the distance between any vertex in $V$ and the closest vertex in $S$ is…
The aim of this paper is twofold. Firstly, we give easy-to-handle criteria to determine whether a given family of subsets of a vector space is a neighbourhood basis of the origin for a complete vector topology. Then, we apply these criteria…
We present an invertible map between correlations in any bipartite Bell scenario and behaviours in a family of contextuality scenarios. The map takes local, quantum and non-signalling correlations to non-contextual, quantum and contextual…
We consider the maximal number of arbitrary points in a special fibre that can be simultaneously approached by points in one sequence of general fibres. Several results about this topological invariant and their applications describe the…
The authors claim that they "strictly" closed locality loophole, but their work does not close the locality loophole. there are at least two local transinformation explanations. The two explanations are the counter-examples of their claim.…
For each $p>n$ we use local oscillations and doubling measures to give intrinsic characterizations of the restriction of the Sobolev space $W_p^1(R^n)$ to an arbitrary closed subset of $R^n$.
The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.
The beta transformation is the iterated map $\beta x\,\mod1$; it generates the base-$\beta$ expansion of a real number x. Every iterated piece-wise monotonic map is topologically conjugate to the beta transformation. For all but a countable…
While topology given by a linear order has been extensively studied, this cannot be said about the case when the order is given only locally. The aim of this paper is to fill this gap. We consider relation between local orderability and…
Let $D$ be a two-dimensional regular local ring. We prove there is a one-to-one correspondence between closed connected sets in the space of valuation overrings of $D$ that dominate $D$ and the integrally closed local overrings of $D$ that…
In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the convex case. Then we apply this machinery to deriving new…
Let $X$ be a set and $2^X$ be a set of all subsets of $X$. The necessary and sufficient conditions under which a mapping $X \to 2^X$ is a closure of one-point sets in some $T_0$-space $(X, \tau)$ are described. It is proved that every…
The aim of this survey article is to cover most of the recent research on preopen sets. I try to present majority of the results on preopen sets that I am aware of.
It is well known that \omega-limit sets are internally chain transitive and have weak incompressibility; the converse is not generally true, in either case. However, it has been shown that a set is weakly incompressible if and only if it is…
Abstract Equivalent conditions that make the convex subdifferential maximal monotone are investigated in the general settings of locally convex spaces.
A contractive condition is addressed for extended 2-cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same subsets of its domain. It is…
We present examples of closed subsets of a free group such that their product is not closed in the profinite topology. We discuss how to characterize a subset of a free group which is closed in the profinite topology and its product with…
We give a criterium when a linearly ordered topological semilattice is $H$-closed. We also prove that any linearly ordered $H$-closed topological semilattice is absolutely $H$-closed and we show that every linearly ordered semilattice is a…
Let $\beta_1,\beta_2>1$ and $T_i(x,y) = \bigl(\frac{x+i}{\beta_1}, \frac{y+i}{\beta_2}\bigr),\ i\in\{\pm1\}$. Let $A := A_{\beta_1, \beta_2}$ be the unique compact set satisfying $A = T_{1}(A) \cup T_{-1}(A)$. In this paper we give a…
We prove that for the functions of the form $g(x) = h(x) + \frac{C}{x+i}$, where $h$ belongs to the continuous Wiener algebra $W_0$, the intersection of the frame set $\mathcal{F}_g$ with every hyperbola $\{\alpha, \beta > 0 \mid…