4 problems

Let $G$ be a definably compact group, let $M_0$ be the parameter structure over which $G$ is defined, and let $G^{00}$ denote the infinitesimal subgroup. Contractibility conjecture…

Let $(X,\tau)$ be a definable topological space in an o-minimal expansion of an ordered field. Call $(X,\tau)$ affine if it is definably homeomorphic to a set with the o-minimal Eu…

Let $S \subset K \subset \mathbb R^n$ be a bounded definable set with a monotone family of compact sets $\{S_\delta\}_{\delta>0}$ satisfying $S=\bigcup_\delta S_\delta$. Suppose th…

Covering conjecture. Every definable set is a finite union of relatively open definable subsets which are definably simply connected.