- Decomposability conjecture:
Can we generalize the Jayne-Rogers theorem to higher Borel ranks?
- Second-level Borel isomorphism types of strongly infinite dimensional compacta:
Does every strongly infinite dimensional compactum second-level Borel isomorphic to the Hilbert cube?
- First-level Borel isomorphism types of arc-like continua:
How many first-level Borel isomorphism types of arc-like continua do there exist?
- The existence of a non-σ-punctiform space:
Is the Hilbert cube non-σ-punctiform?
- σ-embedding of the Hilbert cube into a T1 space:
Can the Hilbert cube be σ-embedded into the product of countably many copies of ω, each of which is endowed with the cofinite topology?
A half-Cohen real in computability theory:
Develop a forcing with infinite dimensional compact subsets of a Henderson compactum in computability theory.
- Constructing a Cantor manifold in a Scott ideal:
Let x be a PA degree. Does every n-dimensional co-c.e. closed subset of the Hilbert cube have an n-dimensional Cantor manifold which is co-c.e. relative to x?
Iterates of choosing points from convex sets:
Is the third iterate of the convex choice principle Weihrauch reducible to some finite parallel use of the second iterate?
Computability of points in locally contractible continua:
Does every contractible, locally contractible, co-c.e., planar, continuum contain a computable point?