Related papers: Brouwer and Cardinalities
Working in the context of $\mu$-abstract elementary classes ($\mu$-AECs) - or, equivalently, accessible categories with all morphisms monomorphisms - we examine the two natural notions of size that occur, namely cardinality of underlying…
Combining ideas from two of our previous papers, we refine Arhangel'skii Theorem by proving a cardinal inequality of which this is a special case: any increasing union of strongly discretely Lindelof spaces with countable free sequences and…
These are notes for a graduate-level introductory course on singularity categories.
We address ZFC inequalities between some cardinal invariants of the continuum, which turned to be true in spite of strong expectations given by [RoSh:470].
We introduce the notion of $\mathcal{C}$-system of filters, generalizing the standard definitions of both extenders and towers of normal ideals. This provides a framework to develop the theory of extenders and towers in a more general and…
These lecture notes discuss classical models of liquid crystals, and the different ways in which defects are described according to the different models.
In this short paper, we establish the local Noetherian property for the linear categories of Brauer, partition algebras, and other related categories of diagram algebras with no restrictions on their various parameters.
A theory of spline quadrature rules for arbitrary continuity class in a closed interval $[a, b]$ with arbitrary nonuniform subintervals based on semi-classical orthogonal Jacobi polynomials is proposed. For continuity class $c \ge 2$ this…
The present paper is devoted to study some completeness properties of transitive binary relational set, i.e., a set together with a transitive binary relation (so called t-set).
In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.
The first seeds of mathematical intuitionism germinated in Europe over a century ago in the constructive tendencies of Borel, Baire, Lebesque, Poincar\'e, Kronecker and others. The flowering was the work of one man, Luitzen Egbertus Jan…
In this note I make some comments on the review MR2723767 (2011m:03064) appeared in Mathematical Reviews
The implications of the original misunderstanding of the etymology of the word "ergodic" are discussed, and the contents of a not too well known paper by Boltzmann are critically examined. The connection with the modern theory of Ruelle is…
We investigate negative square-brackets partition relations at successors of singular cardinals of countable cofinality. Along the way we prove some club-guessing results.
We consider the class of compact countable subsets of the real numbers $\mathbb{R}$. By using an appropriate partition, up to homeomorphism, of this class we give a detailed proof of a result shown by S. Mazurkiewicz and W. Sierpinski…
Koivisto studied the partitioning of sets of bounded cardinality. We improve his time analysis somewhat, for the special case of triangle partitions, and obtain a slight improvement.
Given a nonempty finite multiset $S$ of positive integers, we wish to find a partially ordered set $P$ of minimal cardinality such that the multiset of cardinalities of all maximal chains in $P$ equals $S$. This paper establishes upper and…
We provide upper bounds for the cardinality of the value set of a polynomial map in several variables over a finite field. These bounds generalize earlier bounds for univariate polynomials.
This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.
Although Bolzano's concept of the continuum has gradually evolved, the basis remained the same: the continuum as an infinite class of points arranged in such a way that the so-called \emph{Bolzano completeness} holds. Bolzano realized over…