  In this paper we give an answer to Furstenberg's problem on topological
disjointness. Namely, we show that a transitive system $(X,T)$ is disjoint from
all minimal systems if and only if $(X,T)$ is weakly mixing and there is some
countable dense subset $D$ of $X$ such that for any minimal system $(Y,S)$, any
point $y\in Y$ and any open neighbourhood $V$ of $y$, and for any nonempty open
subset $U\subset X$, there is $x\in D\cap U$ satisfying that $\{n\in{ \mathbb
Z}_+: T^nx\in U, S^ny\in V\}$ is syndetic. Some characterization for the
general case is also described.
  As applications we show that if a transitive system $(X,T)$ is disjoint from
all minimal systems, then so are $(X^n,T^{(n)})$ and $(X, T^n)$ for any $n\in {
\mathbb N}$. It turns out that a transitive system $(X,T)$ is disjoint from all
minimal systems if and only if the hyperspace system $(K(X),T_K)$ is disjoint
from all minimal systems.
