Compact spaces that do not map onto finite products

We provide examples of nonseparable compact spaces with the property that any continuous image which is homeomorphic to a finite product of spaces has a maximal prescribed number of nonseparable factors

The number of weakly compact convex subsets of the Hilbert space

We prove that for k an uncountable cardinal, there exist 2^k many non homeomorphic weakly compact convex subsets of weight k in the Hilbert space of density k

Extension operators on balls and on spaces of finite sets

We study extension operators between spaces $\sigma_n(2^X)$ of subsets of $X$ of cardinality at most $n$. As an application, we show that if $B_H$ is the unit ball of a nonseparable Hilbert space $H$, equipped with the weak topology, then, for any $0<\lambda<\mu$, there is no extension operator $T: C(\lambda B_H)\to C(\mu B_H)$