We study the cofinal diversity of analytic p-ideals and analytic relative σ-ideals of compact sets. We prove that the σ-ideal of compact meager sets is not cofinally simpler than the asymptotic density zero ideal; this concludes the study of the cofinal types of classical analytic ideals. We obtain this result by using a Ramsey-type partition calculus, which allows us to capture the relevant co...

This is the second part of a paper about the classification of 2-compact groups. In the first part we set up a general classification procedure and applied it to the simple 2-compact groups of the A-family. In this second part we deal with the other simple Lie groups and with the exotic simple 2-compact group DI(4). We show that all simple 2-compact groups are uniquely N -determined and conclud...

in this paper‎, ‎we introduce the notion of $(m,n)$-‎algebr‎aically compact modules as an analogue of algebraically‎ ‎compact modules and then we show that $(m,n)$-algebraically‎ ‎compactness‎ ‎and $(m,n)$-pure injectivity for modules coincide‎. ‎moreover‎, ‎further characterizations of a‎ ‎$(m,n)$-pure injective module over a commutative ring are given‎.

We prove that in Polish, abelian, non-locally-compact groups the family of Haar null sets of Christensen does not fulfil the countable chain condition, that is, there exists an uncountable family of pairwise disjoint universally measurable sets which are not Haar null. (Dougherty, answering an old question of Christensen, showed earlier that this was the case for some Polish, abelian, non-local...

Given a non-degenerate Peano continuum X, a dimension function D : 2∗ → [0,∞] defined on the family 2 X ∗ of compact subsets of X, and a subset Γ ⊂ [0,∞), we recognize the topological structure of the system 〈2 ,D≤γ(X)〉α∈Γ, where 2 X is the hyperspace of non-empty compact subsets of X and D≤γ(X) is the subspace of 2 X , consisting of non-empty compact subsets K ⊂ X with D(K) ≤ γ.

the polarimetric entropy and the alpha angle are two important parameters for analyzing polarimetric synthetic aperture radar data. they demonstrate the degree of randomness in the polarization of the received signal and scattering mechanism of scatterers respectively. recently, there has been an increasing interest in compact polarimetry due to its advantages in comparison with full polarimetr...

We investigate relative holomorphic connections on a principal bundle over family of compact complex manifolds. A sufficient condition is given for the existence connection analytic family. also introduce notion equivariant bundles and establish its relation with bundles.

The paper presents a first step towards family index theorem for classical self-adjoint boundary value problems. We address here the simplest non-trivial case of manifolds with boundary, namely two-dimensional manifolds. result is an families order elliptic differential operators local conditions, parametrized by points compact topological space $X$. compute $K^1(X)$-valued in terms data over b...