8 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…

Let $K$ be a nonempty Valdivia compact space satisfying the countable chain condition (ccc). Valdivia compacta ccc dichotomy conjecture. Either $K$ has a $G_\delta$ point or $K$ ad…

Hernández's conjecture. The space $X$ cannot have an infinite connected component.

Let $X$ be a compact topological space, and suppose every closed subset of $X$ is a $G_\delta$ set, meaning a countable intersection of open subsets of $X$. Fremlin's two-to-one co…

Fremlin's conjecture. The assertion is consistent with ZFC:

Nonexistence conjecture. $\operatorname{MA}+\neg\operatorname{CH}$ implies that there are no pseudo-Aronszajn compacta that are ccc.

A compact space $X$ is Corson compact if and only if it embeds in some $C_p(L(\kappa))$, where $L(\kappa)$ has a $1$-ordered cover by $<\!\aleph_1$-compact sets. A point additively…

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…