Related papers: Generalized heredity in $\mathcal B$-free systems

Let $(X, T)$ be a topological dynamical system (TDS), and $h (T, K)$ the topological entropy of a subset $K$ of $X$. $(X, T)$ is {\it lowerable} if for each $0\le h\le h (T, X)$ there is a non-empty compact subset with entropy $h$; is {\it…

Let $X$ be a normal complex projective variety, $T\subseteq X$ a subvariety, $a\colon X\rightarrow A$ a morphism to an abelian variety such that $\rm{Pic}^0(A)$ injects into $\rm{Pic}^0(T)$ and let $L$ be a line bundle on $X$. Denote by…

In the first part of the paper we present and discuss concepts of local and asymptotic hereditary proximity to \ell_1. The second part is devoted to a complete separation of the hereditary local proximity to \ell_1 from the asymptotic one.…

We investigate the question of when a topological space $X$ has the $\textit{Generalized Bolzano-Weierstrass property}$: every sequence of subsets of $X$ has a convergent subsequence (in the sense of Kuratowski).

For a quasi-projective scheme $X$ admitting a smooth compactification over a local field of residue characteristic $p > 0$, we construct a continuous reciprocity homomorphism from a tame class group to the abelian tame etale fundamental…

Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$. Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is…

The notion of hereditarily equivalent continua is classical in continuum theory with only two known nondegenerate examples (arc, and pseudoarc). In this paper we introduce generically hereditarily equivalent continua, i.e. continua which…

In this paper we characterize tame dynamical systems and functions in terms of eventual non-sensitivity and eventual fragmentability. As a notable application we obtain a neat characterization of tame subshifts $X \subset \{0,1\}^{\mathbb…

Let $(X,d)$ be a compact metric space, $f:X \mapsto X$ be a continuous map satisfying a property we call almost specification (which is slightly weaker than the $g$-almost product property of Pfister and Sullivan), and $\phi$ be a…

We study the cohomology of symbolic dynamical systems called homshifts: they are the nearest-neighbour $\mathbb{Z}^d$ shifts of finite type whose adjacency rules are the same in every direction. Building on the work of Klaus Schmidt…

In this work, we investigate the dynamics of a general non-autonomous system generated by a commutative family of homeomorphisms. In particular, we investigate properties such as periodicity, equicontinuity, minimality and transitivity for…

Let $\mathfrak{i}$ denote the minimal cardinality of a maximal independent family and let $\mathfrak{a}_T$ denote the minimal cardinality of a maximal family of pairwise almost disjoint subtrees of $2^{<\omega}$. Using a countable support…

The foundations of Ringel duality for split quasi-hereditary algebras over commutative Noetherian rings are strengthened. Several descriptions and properties of the smallest resolving subcategory containing all standard modules over split…

Many applications, e.g. in content recommendation, sports, or recruitment, leverage the comparisons of alternatives to score those alternatives. The classical Bradley-Terry model and its variants have been widely used to do so. The…

Let X be compact abelian group and G its dual (a discrete group). If B is an infinite subset of G, let C_B be the set of all x in X such that <phi(x) : phi \in B> converges to 1. If F is a free filter on G, let D_F be the union of all the…

Let $G$ be a countable residually finite group (for instance $\mathbb{F}_2$) and let $\overleftarrow{G}$ be a totally disconnected metric compactification of $G$ equipped with the action of $G$ by left multiplication. For every $r\geq 1$ we…

Let $H$ be an infinite-dimensional Hilbert space. We prove that every unconditional Schauder frame for $H$ contains a subsequence that can be normalized to form a frame for $H$. As a consequence, every semi-normalized unconditional Schauder…

We completely characterize by finding necessary and sufficient conditions those co-Bassian and generalized co-Bassian Abelian groups having, respectively, the hereditary or the super property, thus giving a new insight in the full discovery…

Let H be a complex infinite dimensional Hilbert space. We describe the form of all *-semigroup endomorphisms $\phi$ of B(H) which are uniformly continuous on every commutative C*-subalgebra. In particular, we obtain that if $\phi$ satisfies…

In the following text for arbitrary $X$ with at least two elements, nonempty set $\Gamma$ and self-map $\varphi:\Gamma\to\Gamma$ we prove the set-theoretical entropy of generalized shift $\sigma_\varphi:X^\Gamma\to X^\Gamma$…