Related papers: A remark on $\beta$-locally closed sets

Model sets are always Meyer sets, but not vice-versa. This article is about characterizing model sets (general and regular) amongst the Meyer sets in terms of two associated dynamical systems. These two dynamical systems describe two very…

We revisit the known problem whether each compact topology is contained in a maximal compact topology and collect some partial answers to this question. For instance we show that each compact topology is contained in a compact topology in…

We introduce the notion of an extremal subset in a geodesically complete space with curvature bounded above, i.e., a GCBA space. This is an analogue of an extremal subset in an Alexandrov space with curvature bounded below introduced by…

The Chabauty space of a topological group is the set of its closed subgroups, endowed with a natural topology. As soon as $n>2$, the Chabauty space of $R^n$ has a rather intricate topology and is not a manifold. By an investigation of its…

We show that the statement ``In every separable pseudometric space there is a maximal non-strictly \delta-separated set.'' implies the axiom of choice for countable families of sets. This gives answers to a question of Dybowski and…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

In this paper we consider the unbounded local completely positive and local completely contractive maps on maximal tensor product of unital locally C*-algebras and discuss on extremal points of certain convex subsets in the set of such…

It is proved that any countable topological vector space over a finite field $\mathbb F_p$ or, equivalently, any countable Abelian topological group of prime exponent has a closed discrete basis.

We study finite systems of subspaces of a complex Hilbert space such that each pair of subspaces satisfies a certain condition as described in the following. For each subspace excepting the first one an angle between this subspace and the…

We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…

The aim of this paper is to investigate the intersection problem between two linear sets in the projective line over a finite field. In particular, we analyze the intersection between two clubs with eventually different maximum fields of…

Directional notions in topology and analysis naturally lead to nonsymmetric structures such as quasi-metrics, quasi-uniformities, and modular spaces. In these settings, classical notions of connectedness and completion based on symmetric…

This is a sequel to my paper "The Octagonal PET I: Renormalization and Hyperbolic Symmetry". In this paper we use the renormalization scheme found in the first paper to classify the limit sets of the systems according to their topology. The…

Any symmetric closed subset of a finite crystallographic root system must be a closed subroot system. This is not, in general, true for real affine root systems. In this paper, we determine when this is true and also give a very explicit…

We consider the concept of a local set of inference rules. A local rule set can be automatically transformed into a rule set for which bottom-up evaluation terminates in polynomial time. The local-rule-set transformation gives…

This note initiates an investigation of packing links into a region of Euclidean space to achieve a maximal density subject to geometric constraints. The upper bounds obtained apply only to the class of homotopically essential links and…

Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of…

We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…

Let E be a locally solid vector lattice. In this paper, we consider two particular vector subspaces of the space of all order bounded operators on E. With the aid of two appropriate topologies, we show that under some conditions, they…

We produce a criterion for open sets in projective $n$-space over a separably closed field to have \'etale cohomological dimension bounded by $2n-3$. We use the criterion to exhibit a scheme for which \'etale cohomological dimension is…