Related papers: Monolithic spaces of measures

We construct a compact Hausdorff space $K$ such that the space $P(K)$ of Radon probabiblity measures on $K$ considered with the weak$^*$ topology (induced from the space of continuous functions $C(K)$) is countably tight which is a…

Given a compact space $K$, we denote by $P(K)$ the space of all Radon probability measures on $K$, equipped with the $weak^\ast$ topology inherited from $C(K)^\ast$. For nonmetrizable compacta $K$ even basic properties of $P(K)$ spaces…

We prove that if $K$ is a compact space and the space $P(K\times K)$ of regular probability measures on $K\times K$ has countable tightness in its $weak^*$ topology, then $L_1(\mu)$ is separable for every $\mu\in P(K)$. It has been known…

Locally compact separable metrizable spaces are characterized among all metrizable spaces as those that admit a cofinal sequence $K_1\subset K_2\subset\cdots$ of compact subsets. Their \v{C}ech cohomology is well-understood due to Petkova's…

Under Jensen's diamond principle $\diamondsuit$, we construct a simple Efimov space $K$ whose space of nonatomic probability measures $P_{na}(K)$ is first-countable and sequentially compact. These two properties of $P_{na}(K)$ imply that…

A compact space $K$ is Radon-Nikod\'{y}m if there is a lower semi-continuous metric fragmenting $K$. In this note, we show that, under $\diamondsuit (\mathrm{non}{\mathcal{M}})$, there is a Radon-Nikod\'{y}m compact space of weight…

A topological space is almost locally compact if it contains a dense locally compact subspace. We generalize a result from \cite{Ma}, showing that isomorphism on Borel classes of almost locally compact Polish metric structures is always…

In this paper, we show that there are a totally ordered compact K separable (K is Rosenthal compact set), a Hausdorff topology T' on C(K) and two closed subspaces Y1, Y2 of (C(K); Tp) such that (C(K);T') is not universally measurable,…

We study the existence of non-separable compact spaces that support a measure and are small from the topological point of view. In particular, we show that under Martin's axiom there is a non-separable compact space supporting a measure…

We study the class of compact spaces that appear as structure spaces of separable Banach lattices. In other words, we analyze what $C(K)$ spaces appear as principal ideals of separable Banach lattices. Among other things, it is shown that…

Recently there has been interest in pairs of Banach spaces $(E_0,E)$ in an $o-O$ relation and with $E_0^{**}=E$. It is known that this can be done for Lipschitz spaces on suitable metric spaces. In this paper we consider the case of a…

We prove that a compact space $K$ embeds into a $\sigma$-product of compact metrizable spaces ($\sigma$-product of intervals) if and only if $K$ is (strongly countable-dimensional) hereditarily metalindel\"of and every subspace of $K$ has a…

The Noetherian type of a space is the least k for which the space has a k^op-like base, i.e., a base in which no element has k-many supersets. We prove some results about Noetherian types of (generalized) ordered spaces and products…

We show that there is a compact topological space carrying a measure which is not a weak* limit of finitely supported measures but is in the sequential closure of the set of such measures. We construct compact spaces with measures of…

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or…

We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as MS. We discuss some closure properties of MS, and show that some simply defined compact spaces,…

We give a construction under $CH$ of a non-metrizable compact Hausdorff space $K$ such that any uncountable semi-biorthogonal sequence in $C(K)$ must be of a very specific kind. The space $K$ has many nice properties, such as being…

We show that if K is Rosenthal compact which can be represented by functions with countably many discontinuities then every Radon measure on K is countably determined. We also present an alternative proof of the result stating that every…

A dual pair formulation for asymmetric locally convex spaces is developed that strictly generalises the ordinary vector space setting. The concept of a polar topology carries over to the asymmetric case and some familiar results are…

A compact space $X$ is called $\pi$-monolithic if for any surjective continuous mapping $f:X\rightarrow K$ where $K$ is a metrizable compact space there exists a metrizable compact space $T\subseteq X$ such that $f(T)=K$. A topological…