Related papers: Finite basis for analytic strong n-gaps

For every $n \in \mathbb{N}$, we construct a variety of Heyting algebras, whose $n$-generated free algebra is finite but whose $(n+1)$-generated free algebra is infinite.

Using complex methods combined with Baire's Theorem we show that one-sided extendability, extendability and real analyticity are rare phenomena on various spaces of functions in the topological sense. These considerations led us to…

Let $m\geq 3$ be a positive integer. We prove that there are uncountably many non-commensurable metabelian uniform pro-$p$ groups of dimension $m$. Consequently, there are uncountably many non-commensurable finitely presented pro-$p$ groups…

This paper is concerned with the problem of determining the number of division algebras which share the same collection of finite splitting fields. As a corollary we are able to determine when two central division algebras may be…

In this paper, we count all non-isomorphic lattices on $n$ elements, containing four reducible elements and having nullity three. This work is in respect of Birkhoff's open problem (which is NP-complete) of counting all finite lattices on…

Remark.9 in Bose-Dasgupta-Rubin (2002) review states that when a non-negative integer-valued infinitely divisible law has an atom at unity then its support cannot have any gaps. Here one has two questions. (i) Why there are no gaps and (ii)…

For each vector $x\in \ell^{\infty}$, we can define the non-empty compact set $L_x$ of accumulation points of $x$. Given an infinite subset $A$ of $\mathbb{N}\backslash\{1\}$, we can therefore investigate under which conditions on $A$, the…

We prove that there exist weakly countably determined spaces of complexity higher than coanalytic. On the other hand, we also show that coanalytic sets can be characterized by the existence of a cofinal adequate family of closed sets.…

We introduce adequate concepts of expansion of a digraph to obtain a sequential construction of minimal strong digraphs. We characterize the class of minimal strong digraphs whose expansion preserves the property of minimality. We prove…

An arithmetical structure on a finite, connected graph without loops is an assignment of positive integers to the vertices that satisfies certain conditions. Associated to each of these is a finite abelian group known as its critical group.…

We give examples of real Banach spaces with exactly infinite countably many complex structures and with $\omega_1$ many complex structures.

We introduce a class of countable groups by some abstract group-theoretic conditions. It includes linear groups with finite amenable radical and finitely generated residually finite groups with some non-vanishing $\ell^2$-Betti numbers that…

Let $p_n$ denote the $n$-th prime. For any $m\geq 1$, there exist infinitely many $n$ such that $p_{n}-p_{n-m}\leq C_m$ for some large constant $C_m>0$, and $$p_{n+1}-p_n\geq \frac{c_m\log n\log\log n\log\log\log\log n}{\log\log\log n}, $$…

In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.

We apply model theoretic methods to the problem of existence of countable universal graphs with finitely many forbidden connected subgraphs. We show that to a large extent the question reduces to one of local finiteness of an…

Exposed positive maps in matrix algebras define a dense subset of extremal maps. We provide a class of indecomposable positive maps in the algebra of 2n x 2n complex matrices with n>1. It is shown that these maps are exposed and hence…

Adapting a homotopy reconstruction theorem for general metric compacta, we show that every countable metric or ultrametric compact space can be topologically reconstructed as the inverse limit of a sequence of finite $T_0$ spaces which are…

We introduce the notion of the depth of a finite group $G$, defined as the minimal length of an unrefinable chain of subgroups from $G$ to the trivial subgroup. In this paper we investigate the depth of (non-abelian) finite simple groups.…

We determine all finite subgroups of simple algebraic groups that have irreducible centralizers - that is, centralizers whose connected component does not lie in a parabolic subgroup.

In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…