Big Questions
 Decomposability conjecture:
Can we generalize the JayneRogers theorem to higher Borel ranks?
=> Details  Secondlevel Borel isomorphism types of strongly infinite dimensional compacta:
Does every strongly infinite dimensional compactum secondlevel Borel isomorphic to the Hilbert cube?
=> Details  Firstlevel Borel isomorphism types of arclike continua:
How many firstlevel Borel isomorphism types of arclike continua do there exist?
=> Details  The existence of a nonσpunctiform space:
Is the Hilbert cube nonσpunctiform?
=> Details  σembedding of the Hilbert cube into a T_{1} space:
Can the Hilbert cube be σembedded into the product of countably many copies of ω, each of which is endowed with the cofinite topology?
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Small Questions

A halfCohen real in computability theory:
Develop a forcing with infinite dimensional compact subsets of a Henderson compactum in computability theory.=> Details  Constructing a Cantor manifold in a Scott ideal:
Let x be a PA degree. Does every ndimensional coc.e. closed subset of the Hilbert cube have an ndimensional Cantor manifold which is coc.e. relative to x?
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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?
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Computability of points in locally contractible continua:
Does every contractible, locally contractible, coc.e., planar, continuum contain a computable point?
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