Related papers: Hereditary topological diagonalizations and the Me…

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…

We resolve the topological version of the Erd\H{o}s Similarity conjecture introduced previously by Gallagher, Lai and Weber. We show that a set is topologically universal on ${\mathbb R}$ if and only if it is of strong measure zero. As a…

An irreducible complete atomic OML of infinite height cannot both be algebraic and have the covering property. However, Kalmbach's construction provides an example of such an OML that is algebraic and has the 2-covering property, and…

Let $\mathcal B\subseteq\mathbb N$ be a primitive set. We complement results on heredity of the $\mathcal B$-free subshift $X_\eta$ from [arxiv:1509.08010] in two directions: In the proximal case we prove that a subshift $X_\varphi$, which…

Establishing whether an algebra is quasi-hereditary or not is, in general, a difficult problem. In this paper we introduce a sufficient criterion to determine whether a general finite dimensional algebra is quasi-hereditary by showing that…

Given two quasi-hereditary algebras, their tensor product is quasi-hereditary. In this article, we show that given two exact Borel subalgebras for these quasi-hereditary algebras, their tensor product is an exact Borel subalgebra. Moreover,…

We call a triangulated category \emph{hereditary} provided that it is equivalent to the bounded derived category of a hereditary abelian category, where the equivalence is required to commute with the translation functors. If the…

We study the question of when geometric extension algebras are polynomial quasihereditary. Our main theorem is that under certain assumptions, a geometric extension algebra is polynomial quasihereditary if and only if it arises from an even…

For the module category of a hereditary ring, the Ext-orthogonal pairs of subcategories are studied. For each Ext-orthogonal pair that is generated by a single module, a 5-term exact sequence is constructed. The pairs of finite type are…

According to a result of Kocinac and Scheepers, the Hurewicz covering property is equivalent to a somewhat simpler selection property: For each sequence of large open covers of the space one can choose finitely many elements from each cover…

We study selection principles related to bornological covers using the notion of ideals. We consider ideals $\mathcal I$ and $\mathcal J$ on $\omega$ and standard ideal orderings $KB, K$. Relations between cardinality of a base of a…

Let $A$ be a hereditary algebra. We construct a fundamental domain for the cluster category of $A$ inside the category of modules over the duplicated algebra $\bar{A}$ of $A$. We then prove that there exists a bijection between the tilting…

This paper introduces a generalization of the ddc-condition for complex manifolds. Like the dd^c-condition, it admits a diverse collection of characterizations, and is hereditary under various geometric constructions. Most notably, it is an…

We develop axiomatics of highest weight categories and quasi-hereditary algebras in order to incorporate two semi-infinite situations which are in Ringel duality with each other; the underlying posets are either upper finite or lower…

The theorem we prove is a slight strengthening of some results by Just, Miller, Scheepers and Szeptycki [JMSS]. We use the Michael technique instead of the combinatorial approach in the literature. Comments by the submitter: This short…

A set of reals $X$ is $\mathfrak{b}$-concentrated if it has cardinality at least $\mathfrak{b}$ and it contains a countable set $D\subseteq X$ such that each closed subset of $X$ disjoint with $D$ has size smaller than $\mathfrak{b}$. We…

In this paper we investigate hereditarily normal topological groups and their subspaces. We prove that every compact subspace of a hereditarily normal topological group is metrizable. To prove this statement we first show that a…

This article is a continuation of the study of bornological open covers and related selection principles in metric spaces done in (Chandra et al. 2020) using the idea of strong uniform convergence (Beer and Levi, 2009) on bornology. Here we…

In two papers we noted that in common practice many algebraic constructions are defined only `up to isomorphism' rather than explicitly. We mentioned some questions raised by this fact, and we gave some partial answers. The present paper…

We study the congeniality property of algebras, as defined by Bao, He, and Zhang, in order to establish a version of Auslander's theorem for various families of filtered algebras. It is shown that the property is preserved under homomorphic…