关于Rosenthal矩阵的测度

纤维状的罗森塔尔树和树木

Finitely fibered Rosenthal compacta and trees

研究了树的区间拓扑性质。特别是，我们的特点，承认一个2纤维紧化的树，我们提出了两个例子的树的一点紧化是罗森塔尔紧与一定的重赋范性质的空间的连续函数。

正则概率测度空间的可数紧性

Countable tightness in the spaces of regular probability measures

证明了：如果$K$是紧致空间，且$K\times K$上的正则概率测度空间$P(K\times K)$在其$weak^*$拓扑中具有可数紧性，则$L_1(μ)$对每个$μ\in P(K)$是可分的.已知这样的结果是马丁公理MA $(ω_1)$的一个推论。我们的定理有几个后果;特别是，它推广了一个定理，由于布尔甘和Todorčević的措施罗森塔尔lunta。

Weakly Radon-Nikodým Boolean algebras and independent sequences

A compact space is said to be weakly Radon-Nikodým (WRN) if it can be weak*-embedded into the dual of a Banach space not containing $\ell_1$. We investigate WRN Boolean algebras, i.e. algebras whose Stone space is WRN compact. We show that the class of WRN algebras and the class of minimally generated algebras are incomparable. In particular, we construct a minimally generated nonWRN Boolean algebra whose Stone space is a separable Rosenthal compactum, answering in this way a question of W. Marciszewski. We also study questions of J. Rodríguez and R. Haydon concerning measures and the existenc…

Abundance of independent sequences in compact spaces and Boolean algebras

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 $\mathcal{C}^\perp$ as the class of all compact spaces for which every continuous image in $\mathcal{C}$ is metrizable. We study how this operation relates classes where centeredness is scarce with classes where it is abundant (like Eberlein and $ccc$ compacta), and also classes where independence is scarce (most notably weakly Radon-Nikodým compacta) with classes where i…

Dugundji环上的连续函数空间

Spaces of continuous functions over Dugundji compacta

我们证明了对每个权为1的Dugundji紧$K$，巴拿赫空间$C(K)$是1-Plichko，$K$上的概率测度空间$P(K)$是Valdivia紧的.结合这个结果与非Valdivia紧群的存在性，我们回答了Kalenda的一个问题。

关于幂等概率测度函子的完全度量化

On perfect metrizability of the functor of idempotent probability measures

本文证明了作用在范畴内的幂等概率测度的函子及其连续映射是完全度量化的。