6 problems

Let $G$ be a co-compact Kleinian group. Suppose $K \subset \hat{\mathbb{C}}$ is a continuum, meaning a compact connected set, which is disjoint from all of its $G$-translates. Cale…

Let $X$ be a co-existentially closed continuum, meaning a continuum whose associated commutative unital C-algebra $C(X)$ is co-existentially closed. Its first Čech cohomology group…

Let the pseudo-circle be R.H. Bing's pseudo-circle, an infinite continuum that admits minimal homeomorphisms. A map is noninvertible when it is not a homeomorphism, and a map is mi…

Genericity conjecture. $\mathcal{T}(X)$ is generic in $\mathcal{C}(X)$ and $\mathcal{S}(X)$.

Pseudo-circle conjecture. The pseudo-circle admits no minimal noninvertible map; equivalently, it is another nondegenerate continuum that admits a minimal homeomorphism but no mini…

Component-diameter conjecture. If $C$ is a transitive point for $f_*$ on $2^X$, then