17 problems

Computable-modulus conjecture. The function $f$ has a computable modulus of continuity.

Let $\mathsf{NON}$ be the problem discussed in the paper, and let $\mathsf{NON}^\omega$ and $\mathsf{NON}^\infty$ denote its countable and inverse-limit iterations, respectively. T…

Decidability–clopenness conjecture. Every $\Lambda_{WP}$-decidable property of $\mathcal{G}_{WP}$ is clopen.

Main conjecture. Any $\Lambda_{WP}$-computable function defined on $\mathcal{G}_{WP}$, with image in any recursive metric space, is continuous.

Assume that $\mathbb{X}$ and $\mathbb{Y}$ are computable metric spaces, that $\{\mu_a\}_{a\in\mathbb{N}^{\mathbb{N}}}$ is a uniformly computable family of probability measures on…

Let $E$ be a uniformly convex, smooth, computable Banach space of dimension two, and let $K\subseteq E$ be bounded, convex, and located, meaning that its distance function is compu…

Let $n$ and $m$ be the parameters for the corresponding Borel measurability levels, and let $\mathbf{X}$ and $\mathbf{Y}$ be Polish represented spaces. Write $\mathfrak{b}$ for the…

Let $n$ and $m$ be the parameters for the corresponding Borel measurability levels, and let $\boldsymbol{X}$ and $\boldsymbol{Y}$ be Polish represented spaces. Write $\mathfrak{b}$…

Let $\beta$ and $\alpha$ be ordinals with $\beta < \alpha$, and let $\mathbf{X}$ be a represented space. Write $\mathbf{X}^{(\alpha)}$ for its $\alpha$-th jump and $\chi^{(\beta)}$…

Let \rm\sffamily CC$_2$ denote connected choice for non-empty connected closed subsets of $[0,1]^2$. For a multi-valued operation $f$, write $\operatorname{id}\times f$ for…

Let \rm\sffamily CC$_2$ denote connected choice for non-empty connected closed subsets of $[0,1]^2$. For a multi-valued operation $f$, write $f\times f$ for two parallel ins…

Let \rm\sffamily CC$_2$ be connected choice for non-empty connected closed subsets of $[0,1]^2$, and let \rm\sffamily C$_{[0,1]}$ be closed choice on the unit interva…

Almost-everywhere computability conjecture. For almost all rational maps $f$ of degree $d\geqslant 2$, $J_f$ is polynomial-time computable.

Computability conjecture. Under these two conditions, $J_f$ is polynomial-time computable by a Turing machine with an oracle for the coefficients of $f$.

Computability conjecture. If $\Omega_f$ does not contain any critical points, then $J_f$ is polynomial-time computable by a Turing machine with an oracle for the coefficients of…

Let $(X,\delta)$ be a represented space, let ${\rm C}_X$ denote closed choice on $X$, and let $\lim$ denote the limit operation on Baire-space names. Non-characterization conjectur…

Let ${\rm UC}_X$ denote the unique closed choice operation on a represented Hausdorff space $X$, and let ${\rm C}_X$ denote closed choice on $X$. For Baire space…