2 problems

Uspenskij's conjecture. Not every $k$-dimensional map $f\colon X\longrightarrow Y$ between compacta admits approximation by $k$-dimensional simplicial maps; equivalently, the answe…

Let $P$ and $Q$ be two cubes, and let $f:V(P)\rightarrow V(Q)$. A cubical map is a map between the corresponding cubical face complexes that sends each cube into a cube. Cubical ap…