5 problems

Let $d,s\geq 1$. Suppose that $L_1,\ldots,L_d$ are linearly ordered compact spaces and there is a continuous surjection … where $K_1,\ldots,K_{d+s}$ are infinite compact spaces. Ma…

Dow's conjecture. Souslin lines obtained by lexicographically ordering a Souslin tree are always functionally countable.

Let $M$ be a compact metrizable space and let $A_f$ be a finite-dimensional algebra. Consider isocones in the almost-commutative algebra ${\cal C}(M)\otimes A_f$. The authors const…

Ultraweak isocone axioms equivalence conjecture. The given set of axioms for $I$ is equivalent to the following conditions: $I$ defines a partial order on the pure state space thro…

Valdivia compactness conjecture. If the weight of $K$ does not exceed $\aleph_1$, every point of uncountable character in $K$ is isolated from one side, and every closed first coun…