Related papers: Weak$^*$ dentability index of spaces $C([0,\alpha]…

For each ordinal $\alpha< \omega_1$, we prove the existence of a separable, reflexive Banach space with a basis and Szlenk index $\omega^{\alpha+1}$ which is universal for the class of separable, reflexive Banach spaces $X$ such that the…

Each continuous weak selection for a space $X$ defines a coarser topology on $X$, called a selection topology. Spaces whose topology is determined by a collection of such selection topologies are called continuous weak selection spaces. For…

A combinatorial principle CECA is formulated and its equivalence with GCH+ certain weakenings of Box_lambda for singular lambda is proved. CECA is used to show that certain ``almost point- < tau'' families can be refined to point- < tau…

We show that an \'etale groupoid which is strongly amenable at infinity is amenable whenever its full and reduced $C^*$-algebras coincide.

The weak mean equicontinuous properties for a countable discrete amenable group $G$ acting continuously on a compact metrizable space $X$ are studied. It is shown that the weak mean equicontinuity of $(X \times X,G)$ is equivalent to the…

We compute CP asymmetries of one-particle inclusive B(s) --> D(s) X decay rates. We find that the weak angle gamma could in principle be extracted from these asymmetries although they are very small. Taking the decay width difference into…

We study long chains of iterated weak* derived sets, that is sets of all weak* limits of bounded nets, of subspaces with the additional property that the penultimate weak* derived set is a proper norm dense subspace of the dual. We extend…

Let C(K) be the Banach space of all continuous functions on a given compact space K. We investigate the w*-sequential closure in C(K)* of the set of all finitely supported probabilities on K. We discuss the coincidence of the Baire…

We rigorously derive weakly nonlinear relation between cosmic density and velocity fields up to third order in perturbation theory. The density field is described by the mass density contrast, $\de$. The velocity field is described by the…

Weak lensing is commonly measured using shear through galaxy ellipticities, or using the effect of magnification bias on galaxy number densities. Here, we report on the first detection of weak lensing magnification with a new, independent…

It follows from a theorem of Rosenthal that a compact space is $ccc$ if and only if every Eberlein continuous image is metrizable. Motivated by this result, for a class of compact spaces $\mathcal{C}$ we define its orthogonal…

We propose the notion of countable decomposability of maps on C*-algebras: a bounded linear map $\varphi : \mathscr{A}\to B(\mathcal{H})$, where $\mathscr{A}$ is a C*-algebra and $\mathcal{H}$ a Hilbert space, will be called countably…

Let $A$ be a unital simple separable exact C$^*$-algebra which is approximately divisible and of real rank zero. We prove that the set of positive elements in $A$ with a fixed non-compact Cuntz class has vanishing homotopy groups. Combined…

Compactification of the 5-dimensional Kaluza-Klein space-time geometry is considered. The space-time geometry is supposed to be discrete, uniform and isotropic. It is shown, that consideration of the space-time geometry as a physical…

We show that if $X$ is a separable locally compact Hausdorff connected space with fewer than $\mathfrak c$ non-cut points, then $X$ embeds into a dendrite $D\subseteq \mathbb R ^2$, and the set of non-cut points of $X$ is a nowhere dense…

The clustering of galaxies and the matter distribution around them can be described using the halo model complemented with a realistic description of the way galaxies populate dark matter haloes. This has been used successfully to describe…

We prove that hereditarily Lindel\"of space which is $F_{\sigma\delta}$ in some compactification is absolutely $F_{\sigma\delta}$. In particular, this implies that any separable Banach space is absolutely $F_{\sigma\delta}$ when equipped…

Following up on previous work, we prove a number of results for C*-algebras with the weak ideal property or topological dimension zero, and some results for C*-algebras with related properties. Some of the more important results include:…

We initiate the study of pointed approximative absolute neighborhood retracts. Our motivation is to generate examples of C*-algebras that behave in unexpected ways with respect to weak semiprojectivity. We consider both weak…

This work is a part of my upcoming thesis [7]. We establish an equiconsistency between (1) weak indestructibility for all $\kappa +2$-degrees of strength for cardinals $\kappa $ in the presence of a proper class of strong cardinals, and (2)…