相关论文: Ideals without ccc

In the paper we introduce a new family of "small" sets which is tightly connected with two well known $\sigma$-ideals: of Haar-null sets and of Haar-meager sets. We define a subset $A$ of a topological group $X$ to be…

Topological structure of minimal sets is studied for a dynamical system $(E,F)$ given by a fibre-preserving, in general non-invertible, continuous selfmap $F$ of a graph bundle $E$. These systems include, as a very particular case,…

For a given clutter $\mathcal{C}$, let $I:=I ( \bar{\mathcal{C}} )$ be the circuit ideal in the polynomial ring $S$. In this paper, we show that the Betti numbers of $I$ and $I + ( \textbf{x}_F )$ are the same in their non-linear strands,…

We extend the Becker--Kechris topological realization and change-of-topology theorems for Polish group actions in several directions. For Polish group actions, we prove a single result that implies the original Becker--Kechris theorems, as…

We prove a result on perfect cliques with respect to countably many G-delta relations on a complete metric space. As an application, we show that a Polish group contains a free subgroup generated by a perfect set as long as it contains any…

The paper contains a description of the maximal ideal spaces (spectra) $\cM_A$ of bi-invariant function algebras $A$ on a compact group $G$. There are natural compatible structures in $\cM_A$: it is a compact topological semigroup with…

A clutter is \emph{$k$-wise intersecting} if every $k$ members have a common element, yet no element belongs to all members. We conjecture that, for some integer $k\geq 4$, every $k$-wise intersecting clutter is non-ideal. As evidence for…

This paper conglomerates our findings on the space $C(X)$ of all real valued continuous functions, under different generalizations of the topology of uniform convergence and the $m$-topology. The paper begins with answering all the…

The framework of a new scale invariant analysis on a Cantor set $C\subset $ $% I=[0,1] $, presented originally in {\it S. Raut and D. P. Datta, Fractals, 17, 45-52, (2009)}, is clarified and extended further. For an arbitrarily small…

Suppose that $X$ is a Polish space, $E$ is a countable Borel equivalence relation on $X$, and $\mu$ is an $E$-invariant Borel probability measure on $X$. We consider the circumstances under which for every countable non-abelian free group…

We initiate the study of the internal structure of C*-algebras associated to a left cancellative semigroup in which any two principal right ideals are either disjoint or intersect in another principal right ideal; these are variously called…

The space of unitary $C_{0}$-semigroups on separable infinite dimensional Hilbert space, when viewed under the topology of uniform weak convergence on compact subsets of $\mathbb{R}_{+}$, is known to admit various interesting residual…

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…

For a discrete group $G$, we use the natural correspondence between ideals in the Boolean algebra $ \mathcal{P}_G$ of subsets of $G$ and closed subsets in the Stone-$\check{C}$ech compactifi-cation $\beta G$ as a right topological semigroup…

The action for a massless particle in 4D Minkowski space has a worldline time-reversing symmetry corresponding to CPT invariance of the quantum theory. The analogous symmetry of the N-extended superparticle is shown to be anomalous when N…

We define a notion of ideal for objects in the category of abstract unitary Cuntz semigroups introduced in [3] and termed Cu$^\sim$. We show that the set of ideals of a Cu$^\sim$-semigroup has a complete lattice structure. In fact, we prove…

Let $L$ be a full-rank lattice in $\mathbb R^d$ and write $L^+$ for the semigroup of all vectors with nonnegative coordinates in $L$. We call a basis $X$ for $L$ positive if it is contained in $L^+$. There are infinitely many such bases,…

Kaplanski's Zero Divisor Conjecture envisions that for a torsion-free group G and an integral domain R, the group ring R[G] does not contain non-trivial zero divisors. We define the length of an element a in R[G] as the minimal non-negative…

We work in the Cantor space $2^\omega$. The results of the paper adhere the following pattern. Let $\mathcal{I}\in \{\mathcal{M}, \mathcal{N}, \mathcal{M}\cap \mathcal{N}, \mathcal{E}\}$ and $T$ be a perfect, uniformly perfect or Silver…

Given a closed ideal I in a C*-algebra A, an ideal J (not necessarily closed) in I, a *-homomorphism \al:A --> M(I) and a map L:J --> A with some properties, based on [3] and [9] we define a C*-algebra O(A,\al,L) which we call the "Crossed…