相关论文: Topological density of ccc Boolean algebras - ever…

In statistics cumulants are defined to be functions that measure the linear independence of random variables. In the non-communicative case the Boolean cumulants can be described as functions that measure deviation of a map between algebras…

We consider the boundary-path groupoids of topological higher-rank graphs. We show that the all such groupoids are topologically amenable. We deduce that the C*-algebras of topological higher-rank graphs are nuclear and prove versions of…

The $\kappa$-density of a cardinal $\mu\ge\kappa$ is the least cardinality of a dense collection of $\kappa$-subsets of $\mu$ and is denoted by $\mathcal D(\mu,\kappa)$. The Singular Density Hypothesis (SDH) for a singular cardinal $\mu$ of…

We show the following result: Assume B is an infinite Boolean Algebra and lambda=d(B). Then s(B*B)$, i.e. s(uf(B)xuf(B))>= lambda$ (if lambda limit - obtained)

The existence of a countably compact group without non-trivial convergent sequences in ZFC alone is a major open problem in topological group theory. We give a ZFC example of a Boolean topological group G without non-trivial convergent…

There is no known model in holography exhibiting a $c$-theorem where the central charges of the dual CFT are distinct. We examine a holographic model of RG flows in a framework where the bulk gravity theory contains higher curvature terms.…

We describe two kinds of regular invariant measures on the boundary path space of a second countable topological graph, which allows us to describe all extremal tracial weights on the graph C$^{*}$-algebra which are not gauge-invariant.…

We prove, assuming Souslin's Hypothesis, that each uncountable subspace of each zero-dimensional monotonically normal compact space contains an uncountable subset of the real line with either the metric, the Sorgenfrey, or the discrete…

In this note we shall generalize the Stone duality between compact totally disconnected spaces and Boolean algebras to a duality between all complete non-Archimedean uniform spaces and Boolean algebras.

Consider an inclusion of diffuse von Neumann algebras A c M . We say that A c M has the absorbing amenability property if for any diffuse subalgebra B c A and any amenable intermediate algebra B c D c M we have that D is contained in A. We…

For a tree $T$, we show that for many positive integer values of $n$, and an integer $s \geq 2$, the higher topological complexity $TC_s$ of the unordered configuration spaces of trees $U\mathcal{C}^nT$, is maximal. In other words, we prove…

We show that if $\kappa \leq \omega$ and there exists a group topology without non-trivial convergent sequences on an Abelian group $H$ such that $H^n$ is countably compact for each $n<\kappa$ then there exists a topological group $G$ such…

We study some variations of the product topology on families of clopen subsets of $2^{\mathbb{N}}\times\mathbb{N}$ in order to construct countable nodec regular spaces (i.e. in which every nowhere dense set is closed) with analytic topology…

(1) Every infinite, Abelian compact (Hausdorff) group K admits 2^|K|-many dense, non-Haar-measurable subgroups of cardinality |K|. When K is nonmetrizable, these may be chosen to be pseudocompact. (2) Every infinite Abelian group G admits a…

We deal with some of problems posed by Monk and related to cardinal invariant of ultraproducts of Boolean algebras. We also introduce and investigate some new cardinal invariants.

The topological complexity TC(X) is a homotopy invariant which reflects the complexity of the problem of constructing a motion planning algorithm in the space X, viewed as configuration space of a mechanical system. In this paper we…

We give a canonical construction of a balanced big Cohen-Macaulay algebra for a domain of finite type over $\mathbb C$ by taking ultraproducts of absolute integral closures in positive characteristic. This yields a new tight closure…

The unordered configuration space of $n$ points on a graph $\Gamma,$ denoted here by $UC^n(\Gamma),$ can be viewed as the space of all configurations of $n$ unlabeled robots on a system of one-dimensional tracks, which is interpreted as a…

Assume that there is no quasi-measurable cardinal smaller than $2^\omega$. ($\kappa$ is quasi measurable if there exists $\kappa $-additive ideal $\ci $ of subsets of $\kappa $ such that the Boolean algebra $P(\kappa)/\ci$ satisfies c.c.c.)…

Given a complete atomic Boolean algebra, we show there is a commutative BCK-algebra whose ideal lattice is that Boolean algebra. This result is shown to exist within a larger framework involving BCK-algebras of functions, whose ideals and…