Related papers: On two questions on selectively highly divergent s…

Let (X,d,p) be a pointed metric space. A pretangent space to X at p is a metric space consisting of some equivalence classes of convergent to p sequences (x_n), x_n \in X, whose degree of convergence is comparable with a given scaling…

We call a space $X$ {\it weakly linearly Lindel\"of} if for any family $\mathcal{U}$ of non-empty open subsets of $X$ of regular uncountable cardinality $\kappa$, there exists a point $x\in X$ such that every neighborhood of $x$ meets…

The point selection theorem says that the convex hull of any finite point set contains a point that lies in a positive proportion of the simplices determined by that set. This paper proves several new volumetric versions of this theorem…

We explore the structure of the parameter space in the Singlet Scalar Dark Matter (SSDM) model and the Next-to-Two Higgs Doublet Model (N2HDM) with $\tan\beta = 5$ and $\tan\beta = 45$. Parameter points are classified as allowed or excluded…

I will discuss recent progress by many people in the program of extending natural topological invariants from manifolds to singular spaces. Intersection homology theory and mixed Hodge theory are model examples of such invariants. The past…

Unsupervised semantic segmentation aims to discover groupings within and across images that capture object and view-invariance of a category without external supervision. Grouping naturally has levels of granularity, creating ambiguity in…

Let $X$ be a nondegenerate Peano unicoherent continuum. The family $CB(X)$ of proper subcontinua of $X$ with connected boundaries is a $G_\delta$-subset of the hyperspace $C(X)$ of all subcontinua of $X$. If every nonempty open subset of…

Let $X$ be a set, $\ka$ be a cardinal number and let $\iH$ be a family of subsets of $X$ which covers each $x\in X$ at least $\ka$ times. What assumptions can ensure that $\iH$ can be decomposed into $\kappa$ many disjoint subcovers? We…

The crease set of an event horizon is studied in a spacetime with discrete or continuous symmetry. It determines possible topologies on spatial sections of an event horizon. We thereby investigate the classification of stable topological…

A `discrete differential manifold' we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with a convenient framework for the formulation of…

Convergence spaces are a generalization of topological spaces. The category of convergence spaces is well-suited for Algebraic Topology, one of the reasons is the existence of exponential objects provided by continuous convergence. In this…

Given an $N$-dimensional compact manifold $M$ and a field $\bk$, F. Cohen and L. Taylor have constructed a spectral sequence, $\cE(M,n,\bk)$, converging to the cohomology of the space of ordered configurations of $n$ points in $M$. The…

Given $n$ pairwise disjoint sets $X_1,\ldots, X_n$, we call the elements of $S=X_1\times\ldots\times X_n$ strings. A nonempty set of strings $W\subseteq S$ is said to be well-connected if for every $v\in W$ and for every $i\, (1\le i\le…

In this paper, we shall study categorial properties of the hyperspace of all nontrivial convergent sequences $\mathcal{S}_c(X)$ of a Fre\'ech-Urysohn space $X$, this hyperspace is equipped with the Vietoris topology. We mainly prove that…

Let $D$ be a dictionary in a Hilbert space $H$, that is, a set of unit elements whose linear combinations are dense in $H$. We consider the least $m$-term deviation $\sigma_m(x)$ of an element $x\in H$: this is the distance of $x$ from the…

A set $A \subseteq \mathbb{N}$ is a set of pointwise recurrence if for all minimal dynamical systems $(X, T)$, all $x \in X$, and all open neighborhoods $U \subseteq X$ of $x$, there exists a time $n \in A$ such that $T^n x \in U$. The set…

The following selection theorem is established:\\ Let $X$ be a compactum possessing a binary normal subbase $\mathcal S$ for its closed subsets. Then every set-valued $\mathcal S$-continuous map $\Phi\colon Z\to X$ with closed $\mathcal…

The discrete sell or hold problem (DSHP), which is introduced in \cite{H12}, is studied under the constraint that each asset can only take a constant number of different values. We show that if each asset can take only two values, the…

We study the class $HQ(\mathbb{D})$, the set of harmonic quasiconformal automorphisms of the unit disk $\mathbb{D}$ in the complex plane, endowed with the topology of uniform convergence. Several important topological properties of this…

We use the "closed point sieve" to prove a variant of a Bertini theorem over finite fields. Specifically, given a smooth quasi-projective subscheme X of P^n of dimension m over F_q, and a closed subscheme Z in P^n such that Z intersect X is…